Av(13452, 13542, 14253, 14352, 23451, 23541, 24351, 32451, 32541, 42531)
Counting Sequence
1, 1, 2, 6, 24, 110, 533, 2640, 13195, 66236, 333343, 1680625, 8485014, 42885952, 216953282, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(4 x^{13}-20 x^{12}+4 x^{11}+75 x^{10}-59 x^{9}+157 x^{8}-258 x^{7}-369 x^{6}+300 x^{5}-668 x^{4}+906 x^{3}-437 x^{2}+76 x -4\right) F \left(x
\right)^{3}+\left(-8 x^{13}+48 x^{12}-266 x^{10}+73 x^{9}-74 x^{8}+823 x^{7}+1310 x^{6}-620 x^{5}+798 x^{4}-1891 x^{3}+1120 x^{2}-214 x +12\right) F \left(x
\right)^{2}+\left(-28 x^{12}+48 x^{11}+243 x^{10}-190 x^{9}-404 x^{8}-1059 x^{7}-1235 x^{6}+729 x^{5}-68 x^{4}+1216 x^{3}-944 x^{2}+200 x -12\right) F \! \left(x \right)-20 x^{11}-20 x^{10}+183 x^{9}+314 x^{8}+414 x^{7}+295 x^{6}-333 x^{5}-101 x^{4}-226 x^{3}+261 x^{2}-62 x +4 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 110\)
\(\displaystyle a(6) = 533\)
\(\displaystyle a(7) = 2640\)
\(\displaystyle a(8) = 13195\)
\(\displaystyle a(9) = 66236\)
\(\displaystyle a(10) = 333343\)
\(\displaystyle a(11) = 1680625\)
\(\displaystyle a(12) = 8485014\)
\(\displaystyle a(13) = 42885952\)
\(\displaystyle a(14) = 216953282\)
\(\displaystyle a(15) = 1098331415\)
\(\displaystyle a(16) = 5563635627\)
\(\displaystyle a(17) = 28196538393\)
\(\displaystyle a(18) = 142957765639\)
\(\displaystyle a(19) = 725044812409\)
\(\displaystyle a(20) = 3678265926766\)
\(\displaystyle a(21) = 18664790745007\)
\(\displaystyle a(22) = 94730311829760\)
\(\displaystyle a(23) = 480869898213082\)
\(\displaystyle a(24) = 2441339639517323\)
\(\displaystyle a(25) = 12396007232054418\)
\(\displaystyle a(26) = 62947855496898822\)
\(\displaystyle a(27) = 319682784801027099\)
\(\displaystyle a(28) = 1623646304485289305\)
\(\displaystyle a(29) = 8246942406834062538\)
\(\displaystyle a(30) = 41890930603898454701\)
\(\displaystyle a(31) = 212798855128186187851\)
\(\displaystyle a(32) = 1081030595448553406834\)
\(\displaystyle a(33) = 5491913461940076578122\)
\(\displaystyle a(34) = 27901291110031784212708\)
\(\displaystyle a(35) = 141754882653755280962128\)
\(\displaystyle a(36) = 720216887196321517610688\)
\(\displaystyle a(37) = 3659306277362102851025707\)
\(\displaystyle a(38) = 18592732596311098563421907\)
\(\displaystyle a(39) = 94470378030518843771780140\)
\(\displaystyle a(40) = 480015371754761901646310289\)
\(\displaystyle a{\left(n + 41 \right)} = \frac{48 n \left(n + 1\right) a{\left(n \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{8 \left(n + 1\right) \left(68 n + 87\right) a{\left(n + 1 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(2092 n + 81577\right) a{\left(n + 40 \right)}}{65 \left(n + 40\right)} + \frac{4 \left(575 n^{2} + 2327 n + 2475\right) a{\left(n + 2 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{6 \left(1146 n^{2} + 9471 n + 18562\right) a{\left(n + 3 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} + \frac{2 \left(14246 n^{2} + 170330 n + 446481\right) a{\left(n + 4 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(71117 n^{2} + 981995 n + 2970495\right) a{\left(n + 5 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(74830 n^{2} + 341113 n + 522678\right) a{\left(n + 6 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(109049 n^{2} + 8378291 n + 160951434\right) a{\left(n + 39 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(299562 n^{2} + 3869893 n + 13255956\right) a{\left(n + 7 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(775492 n^{2} + 58503172 n + 1103925129\right) a{\left(n + 38 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(1648334 n^{2} + 24991832 n + 99894939\right) a{\left(n + 8 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(2478993 n^{2} + 181820461 n + 3338439829\right) a{\left(n + 37 \right)}}{520 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(7501609 n^{2} + 139174087 n + 667981986\right) a{\left(n + 9 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(10531498 n^{2} + 219131848 n + 1151032935\right) a{\left(n + 10 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(21823285 n^{2} + 1531367504 n + 26910465632\right) a{\left(n + 36 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(34988995 n^{2} + 710007406 n + 3727952193\right) a{\left(n + 11 \right)}}{520 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(85491613 n^{2} - 5803741065 n - 136110407702\right) a{\left(n + 20 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(179189789 n^{2} + 9236352198 n + 115214266671\right) a{\left(n + 32 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(194083211 n^{2} + 13095586821 n + 220942827520\right) a{\left(n + 35 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(197267944 n^{2} + 4327024633 n + 24348949200\right) a{\left(n + 12 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(296186006 n^{2} + 7054542707 n + 43477800744\right) a{\left(n + 13 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(469176306 n^{2} + 14796849517 n + 118579027026\right) a{\left(n + 17 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(511646803 n^{2} + 13653683533 n + 93420744270\right) a{\left(n + 15 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(742827941 n^{2} + 19560200798 n + 131794453440\right) a{\left(n + 14 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(872918867 n^{2} + 59547662191 n + 1006817338960\right) a{\left(n + 33 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(939763469 n^{2} + 62233677179 n + 1028656930458\right) a{\left(n + 34 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(1246942378 n^{2} + 64728418714 n + 798527025729\right) a{\left(n + 21 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(1896889535 n^{2} - 42705271675 n - 2199234861468\right) a{\left(n + 26 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(2189424895 n^{2} + 67567922767 n + 525996903594\right) a{\left(n + 16 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(3089079842 n^{2} + 174127568642 n + 2445439344723\right) a{\left(n + 31 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(3546136137 n^{2} + 148891464148 n + 1570240000593\right) a{\left(n + 22 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(9102921295 n^{2} + 302101701511 n + 2537338090482\right) a{\left(n + 18 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(10793111029 n^{2} + 376386071089 n + 3316498060410\right) a{\left(n + 19 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(19183036982 n^{2} + 1042729402793 n + 14127752234397\right) a{\left(n + 27 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(23258523640 n^{2} + 1299773116495 n + 18123643345914\right) a{\left(n + 30 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(24674762767 n^{2} + 1046564330791 n + 10963705091520\right) a{\left(n + 25 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(27363593290 n^{2} + 1505959179490 n + 20700774595461\right) a{\left(n + 29 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(31627623641 n^{2} + 1369478649539 n + 14856545884428\right) a{\left(n + 24 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(40954459541 n^{2} + 1771917033455 n + 19251903033498\right) a{\left(n + 23 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(54957121315 n^{2} + 2986480898503 n + 40560656187084\right) a{\left(n + 28 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)}, \quad n \geq 41\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 110\)
\(\displaystyle a(6) = 533\)
\(\displaystyle a(7) = 2640\)
\(\displaystyle a(8) = 13195\)
\(\displaystyle a(9) = 66236\)
\(\displaystyle a(10) = 333343\)
\(\displaystyle a(11) = 1680625\)
\(\displaystyle a(12) = 8485014\)
\(\displaystyle a(13) = 42885952\)
\(\displaystyle a(14) = 216953282\)
\(\displaystyle a(15) = 1098331415\)
\(\displaystyle a(16) = 5563635627\)
\(\displaystyle a(17) = 28196538393\)
\(\displaystyle a(18) = 142957765639\)
\(\displaystyle a(19) = 725044812409\)
\(\displaystyle a(20) = 3678265926766\)
\(\displaystyle a(21) = 18664790745007\)
\(\displaystyle a(22) = 94730311829760\)
\(\displaystyle a(23) = 480869898213082\)
\(\displaystyle a(24) = 2441339639517323\)
\(\displaystyle a(25) = 12396007232054418\)
\(\displaystyle a(26) = 62947855496898822\)
\(\displaystyle a(27) = 319682784801027099\)
\(\displaystyle a(28) = 1623646304485289305\)
\(\displaystyle a(29) = 8246942406834062538\)
\(\displaystyle a(30) = 41890930603898454701\)
\(\displaystyle a(31) = 212798855128186187851\)
\(\displaystyle a(32) = 1081030595448553406834\)
\(\displaystyle a(33) = 5491913461940076578122\)
\(\displaystyle a(34) = 27901291110031784212708\)
\(\displaystyle a(35) = 141754882653755280962128\)
\(\displaystyle a(36) = 720216887196321517610688\)
\(\displaystyle a(37) = 3659306277362102851025707\)
\(\displaystyle a(38) = 18592732596311098563421907\)
\(\displaystyle a(39) = 94470378030518843771780140\)
\(\displaystyle a(40) = 480015371754761901646310289\)
\(\displaystyle a{\left(n + 41 \right)} = \frac{48 n \left(n + 1\right) a{\left(n \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{8 \left(n + 1\right) \left(68 n + 87\right) a{\left(n + 1 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(2092 n + 81577\right) a{\left(n + 40 \right)}}{65 \left(n + 40\right)} + \frac{4 \left(575 n^{2} + 2327 n + 2475\right) a{\left(n + 2 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{6 \left(1146 n^{2} + 9471 n + 18562\right) a{\left(n + 3 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} + \frac{2 \left(14246 n^{2} + 170330 n + 446481\right) a{\left(n + 4 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(71117 n^{2} + 981995 n + 2970495\right) a{\left(n + 5 \right)}}{65 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(74830 n^{2} + 341113 n + 522678\right) a{\left(n + 6 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(109049 n^{2} + 8378291 n + 160951434\right) a{\left(n + 39 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(299562 n^{2} + 3869893 n + 13255956\right) a{\left(n + 7 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(775492 n^{2} + 58503172 n + 1103925129\right) a{\left(n + 38 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(1648334 n^{2} + 24991832 n + 99894939\right) a{\left(n + 8 \right)}}{130 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(2478993 n^{2} + 181820461 n + 3338439829\right) a{\left(n + 37 \right)}}{520 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(7501609 n^{2} + 139174087 n + 667981986\right) a{\left(n + 9 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(10531498 n^{2} + 219131848 n + 1151032935\right) a{\left(n + 10 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(21823285 n^{2} + 1531367504 n + 26910465632\right) a{\left(n + 36 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(34988995 n^{2} + 710007406 n + 3727952193\right) a{\left(n + 11 \right)}}{520 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(85491613 n^{2} - 5803741065 n - 136110407702\right) a{\left(n + 20 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(179189789 n^{2} + 9236352198 n + 115214266671\right) a{\left(n + 32 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(194083211 n^{2} + 13095586821 n + 220942827520\right) a{\left(n + 35 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(197267944 n^{2} + 4327024633 n + 24348949200\right) a{\left(n + 12 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(296186006 n^{2} + 7054542707 n + 43477800744\right) a{\left(n + 13 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(469176306 n^{2} + 14796849517 n + 118579027026\right) a{\left(n + 17 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(511646803 n^{2} + 13653683533 n + 93420744270\right) a{\left(n + 15 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(742827941 n^{2} + 19560200798 n + 131794453440\right) a{\left(n + 14 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{3 \left(872918867 n^{2} + 59547662191 n + 1006817338960\right) a{\left(n + 33 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(939763469 n^{2} + 62233677179 n + 1028656930458\right) a{\left(n + 34 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(1246942378 n^{2} + 64728418714 n + 798527025729\right) a{\left(n + 21 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(1896889535 n^{2} - 42705271675 n - 2199234861468\right) a{\left(n + 26 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(2189424895 n^{2} + 67567922767 n + 525996903594\right) a{\left(n + 16 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(3089079842 n^{2} + 174127568642 n + 2445439344723\right) a{\left(n + 31 \right)}}{260 \left(n + 39\right) \left(n + 40\right)} + \frac{3 \left(3546136137 n^{2} + 148891464148 n + 1570240000593\right) a{\left(n + 22 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(9102921295 n^{2} + 302101701511 n + 2537338090482\right) a{\left(n + 18 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(10793111029 n^{2} + 376386071089 n + 3316498060410\right) a{\left(n + 19 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(19183036982 n^{2} + 1042729402793 n + 14127752234397\right) a{\left(n + 27 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(23258523640 n^{2} + 1299773116495 n + 18123643345914\right) a{\left(n + 30 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(24674762767 n^{2} + 1046564330791 n + 10963705091520\right) a{\left(n + 25 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(27363593290 n^{2} + 1505959179490 n + 20700774595461\right) a{\left(n + 29 \right)}}{1040 \left(n + 39\right) \left(n + 40\right)} + \frac{\left(31627623641 n^{2} + 1369478649539 n + 14856545884428\right) a{\left(n + 24 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(40954459541 n^{2} + 1771917033455 n + 19251903033498\right) a{\left(n + 23 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)} - \frac{\left(54957121315 n^{2} + 2986480898503 n + 40560656187084\right) a{\left(n + 28 \right)}}{2080 \left(n + 39\right) \left(n + 40\right)}, \quad n \geq 41\)
This specification was found using the strategy pack "Point And Row Placements Req Corrob" and has 134 rules.
Finding the specification took 2284 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{18}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{56}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x^{2} F_{9} \left(x \right)^{3}-x^{2} F_{9} \left(x \right)^{2}+F_{9} \left(x \right)^{2} x +1\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{12}\! \left(x \right) &= 0\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x\\
F_{19}\! \left(x \right) &= 2 F_{12}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{18}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{32}\! \left(x \right) &= x^{2} F_{32} \left(x \right)^{3}+2 x^{2} F_{32} \left(x \right)^{2}+x^{2} F_{32}\! \left(x \right)+x F_{32} \left(x \right)^{2}+2 x F_{32}\! \left(x \right)+x\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{27}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{2}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{18}\! \left(x \right) F_{39}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{18}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{18}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{18}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{122}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= -F_{120}\! \left(x \right)-2 F_{12}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= \frac{F_{63}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{113}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{67}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{18}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{18}\! \left(x \right) F_{70}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{18}\! \left(x \right) F_{71}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{9} \left(x \right)^{2} F_{18}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{18}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{18}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{18}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{71}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{18}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{18}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{18}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{18}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{77}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{71}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{74}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{18}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{106}\! \left(x \right) F_{18}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{18}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{12}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{18}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{2}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= \frac{F_{128}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{128}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{64}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row And Col Placements Req Corrob" and has 152 rules.
Finding the specification took 12024 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{148}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{14}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{15}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{14}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{4}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{14}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= 2 F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{31}\! \left(x \right) &= 0\\
F_{32}\! \left(x \right) &= F_{14}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{14}\! \left(x \right) F_{35}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= -F_{3}\! \left(x \right)-F_{31}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{44}\! \left(x \right) &= x^{2} F_{44} \left(x \right)^{3}-x^{2} F_{44} \left(x \right)^{2}+x F_{44} \left(x \right)^{2}+1\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{44} \left(x \right)^{2} F_{14}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{40}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{14}\! \left(x \right) F_{43}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{53}\! \left(x \right) &= 2 F_{31}\! \left(x \right)+F_{54}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{14}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{14}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right) F_{43}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{14}\! \left(x \right) F_{44}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{40}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{14}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{14}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{4}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{14}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{14}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{14}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{14}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{43}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{44}\! \left(x \right) F_{51}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{51}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{119}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{103}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{14}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{14}\! \left(x \right) F_{43}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{14}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{100}\! \left(x \right) F_{14}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{101}\! \left(x \right) F_{14}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{14}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{116}\! \left(x \right) F_{14}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{14}\! \left(x \right) F_{66}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= -F_{122}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{43}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{14}\! \left(x \right) F_{44}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{132}\! \left(x \right) &= \frac{F_{133}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= -F_{135}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{14}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{14}\! \left(x \right) F_{43}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{14}\! \left(x \right) F_{140}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{145}\! \left(x \right) &= 2 F_{31}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{10}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{14}\! \left(x \right) F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 532 rules.
Finding the specification took 41637 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{23}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{23}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= x^{2} F_{10} \left(x \right)^{3}+2 x^{2} F_{10} \left(x \right)^{2}+x^{2} F_{10}\! \left(x \right)+x F_{10} \left(x \right)^{2}+2 x F_{10}\! \left(x \right)+x\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{530}\! \left(x \right)\\
F_{12}\! \left(x \right) &= -F_{525}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= -F_{146}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{516}\! \left(x \right)\\
F_{17}\! \left(x \right) &= -F_{510}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{23}\! \left(x \right) &= x\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{21}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{23}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{507}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{23}\! \left(x \right) F_{34}\! \left(x \right) F_{505}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{502}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{37}\! \left(x \right) &= x^{2} F_{37} \left(x \right)^{3}-x^{2} F_{37} \left(x \right)^{2}+x F_{37} \left(x \right)^{2}+1\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{23}\! \left(x \right) F_{36}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{37} \left(x \right)^{2} F_{23}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{495}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{498}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{471}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{10}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{436}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= -F_{433}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{23}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{61}\! \left(x \right) &= 0\\
F_{62}\! \left(x \right) &= F_{23}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{23}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{23}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{23}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{23}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{23}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{61}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{23}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{23}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{21}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{82}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{23}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{61}\! \left(x \right)+F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{95}\! \left(x \right) &= 0\\
F_{96}\! \left(x \right) &= F_{23}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{113}\! \left(x \right) &= -F_{432}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{115}\! \left(x \right) &= -F_{118}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{117}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{351}\! \left(x \right)\\
F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{350}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{118}\! \left(x \right) F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{134}\! \left(x \right) &= -F_{21}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{2}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{10}\! \left(x \right) F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{10}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right) F_{23}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{163}\! \left(x \right) &= -F_{169}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= -F_{158}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= \frac{F_{167}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{10}\! \left(x \right) F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{208}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{199}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{190}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{10}\! \left(x \right) F_{181}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{10}\! \left(x \right) F_{177}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{10}\! \left(x \right) F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= \frac{F_{194}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{194}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{174}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right) F_{23}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{203}\! \left(x \right) &= -F_{182}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{199}\! \left(x \right) F_{206}\! \left(x \right) F_{23}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{222}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{146}\! \left(x \right) F_{199}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{199}\! \left(x \right) F_{213}\! \left(x \right) F_{23}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{213}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{216}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{2}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{147}\! \left(x \right) F_{199}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{21}\! \left(x \right) F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= \frac{F_{229}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{229}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{230}\! \left(x \right) &= -F_{247}\! \left(x \right)+F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= \frac{F_{232}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{23}\! \left(x \right) F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{202}\! \left(x \right) F_{23}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= \frac{F_{241}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= -F_{245}\! \left(x \right)+F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= \frac{F_{244}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{244}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{0}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{21}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{214}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{253}\! \left(x \right) &= -F_{347}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{310}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{251}\! \left(x \right) F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)+F_{286}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{23}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{270}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{261}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{23}\! \left(x \right) F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{265}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= x^{2}\\
F_{267}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{23}\! \left(x \right) F_{261}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{23}\! \left(x \right) F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{274}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{275}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{23}\! \left(x \right) F_{271}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{23}\! \left(x \right) F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{23}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{284}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{23}\! \left(x \right) F_{277}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{23}\! \left(x \right) F_{287}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{271}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= 2 F_{61}\! \left(x \right)+F_{291}\! \left(x \right)+F_{304}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{23}\! \left(x \right) F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{298}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{294}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{23}\! \left(x \right) F_{296}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{301}\! \left(x \right)\\
F_{299}\! \left(x \right) &= 2 F_{61}\! \left(x \right)+F_{291}\! \left(x \right)+F_{300}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{23}\! \left(x \right) F_{257}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{302}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{23}\! \left(x \right) F_{303}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{299}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{23}\! \left(x \right) F_{305}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{307}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{299}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{290}\! \left(x \right)+F_{308}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{23}\! \left(x \right) F_{290}\! \left(x \right)\\
F_{310}\! \left(x \right) &= -F_{345}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{323}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{313}\! \left(x \right)+F_{318}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{23}\! \left(x \right) F_{315}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{317}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{118}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{23}\! \left(x \right) F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{321}\! \left(x \right)\\
F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{315}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{344}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{118}\! \left(x \right) F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{327}\! \left(x \right)+F_{329}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{23}\! \left(x \right) F_{331}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)+F_{339}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{10}\! \left(x \right) F_{333}\! \left(x \right)\\
F_{333}\! \left(x \right) &= -F_{334}\! \left(x \right)+F_{240}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{335}\! \left(x \right) &= \frac{F_{336}\! \left(x \right)}{F_{23}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{336}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{338}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{170}\! \left(x \right) F_{20}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{340}\! \left(x \right)+F_{342}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{163}\! \left(x \right) F_{20}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{10}\! \left(x \right) F_{170}\! \left(x \right) F_{20}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{147}\! \left(x \right) F_{317}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{251}\! \left(x \right) F_{346}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{317}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{349}\! \left(x \right)\\
F_{348}\! \left(x \right) &= F_{250}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{349}\! \left(x \right) &= F_{251}\! \left(x \right) F_{257}\! \left(x \right)\\
F_{350}\! \left(x \right) &= F_{2}\! \left(x \right) F_{317}\! \left(x \right)\\
F_{351}\! \left(x \right) &= F_{352}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{379}\! \left(x \right)\\
F_{353}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= F_{355}\! \left(x \right)+F_{356}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{355}\! \left(x \right) &= F_{21}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{23}\! \left(x \right) F_{357}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)+F_{359}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{261}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{360}\! \left(x \right)\\
F_{360}\! \left(x \right) &= 2 F_{61}\! \left(x \right)+F_{361}\! \left(x \right)+F_{373}\! \left(x \right)\\
F_{361}\! \left(x \right) &= F_{23}\! \left(x \right) F_{362}\! \left(x \right)\\
F_{362}\! \left(x \right) &= F_{363}\! \left(x \right)+F_{367}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{364}\! \left(x \right)\\
F_{364}\! \left(x \right) &= F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= F_{23}\! \left(x \right) F_{366}\! \left(x \right)\\
F_{366}\! \left(x \right) &= F_{265}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{370}\! \left(x \right)\\
F_{368}\! \left(x \right) &= 2 F_{61}\! \left(x \right)+F_{361}\! \left(x \right)+F_{369}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{23}\! \left(x \right) F_{354}\! \left(x \right)\\
F_{370}\! \left(x \right) &= F_{371}\! \left(x \right)\\
F_{371}\! \left(x \right) &= F_{23}\! \left(x \right) F_{372}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{368}\! \left(x \right)\\
F_{373}\! \left(x \right) &= F_{23}\! \left(x \right) F_{374}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{376}\! \left(x \right)\\
F_{375}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{368}\! \left(x \right)\\
F_{376}\! \left(x \right) &= F_{360}\! \left(x \right)+F_{377}\! \left(x \right)\\
F_{377}\! \left(x \right) &= F_{378}\! \left(x \right)\\
F_{378}\! \left(x \right) &= F_{23}\! \left(x \right) F_{360}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{380}\! \left(x \right)\\
F_{380}\! \left(x \right) &= 2 F_{61}\! \left(x \right)+F_{381}\! \left(x \right)+F_{409}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{23}\! \left(x \right) F_{382}\! \left(x \right)\\
F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)+F_{393}\! \left(x \right)\\
F_{383}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{384}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{23}\! \left(x \right) F_{386}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{387}\! \left(x \right)+F_{390}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{388}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{23}\! \left(x \right) F_{265}\! \left(x \right)\\
F_{390}\! \left(x \right) &= F_{384}\! \left(x \right)+F_{391}\! \left(x \right)\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{392}\! \left(x \right) &= F_{23}\! \left(x \right) F_{384}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{400}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{395}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{23}\! \left(x \right) F_{396}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{397}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{398}\! \left(x \right)\\
F_{398}\! \left(x \right) &= F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= F_{23}\! \left(x \right) F_{394}\! \left(x \right)\\
F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{23}\! \left(x \right) F_{402}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{403}\! \left(x \right)+F_{406}\! \left(x \right)\\
F_{403}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{404}\! \left(x \right)\\
F_{404}\! \left(x \right) &= F_{405}\! \left(x \right)\\
F_{405}\! \left(x \right) &= F_{23}\! \left(x \right) F_{268}\! \left(x \right)\\
F_{406}\! \left(x \right) &= F_{400}\! \left(x \right)+F_{407}\! \left(x \right)\\
F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{23}\! \left(x \right) F_{400}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{23}\! \left(x \right) F_{410}\! \left(x \right)\\
F_{410}\! \left(x \right) &= F_{411}\! \left(x \right)+F_{412}\! \left(x \right)\\
F_{411}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{394}\! \left(x \right)\\
F_{412}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{413}\! \left(x \right)\\
F_{413}\! \left(x \right) &= 3 F_{61}\! \left(x \right)+F_{414}\! \left(x \right)+F_{426}\! \left(x \right)\\
F_{414}\! \left(x \right) &= F_{23}\! \left(x \right) F_{415}\! \left(x \right)\\
F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{420}\! \left(x \right)\\
F_{416}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{417}\! \left(x \right)\\
F_{417}\! \left(x \right) &= F_{418}\! \left(x \right)\\
F_{418}\! \left(x \right) &= F_{23}\! \left(x \right) F_{419}\! \left(x \right)\\
F_{419}\! \left(x \right) &= F_{268}\! \left(x \right)\\
F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)+F_{423}\! \left(x \right)\\
F_{421}\! \left(x \right) &= 3 F_{61}\! \left(x \right)+F_{414}\! \left(x \right)+F_{422}\! \left(x \right)\\
F_{422}\! \left(x \right) &= F_{23}\! \left(x \right) F_{380}\! \left(x \right)\\
F_{423}\! \left(x \right) &= F_{424}\! \left(x \right)\\
F_{424}\! \left(x \right) &= F_{23}\! \left(x \right) F_{425}\! \left(x \right)\\
F_{425}\! \left(x \right) &= F_{421}\! \left(x \right)\\
F_{426}\! \left(x \right) &= F_{23}\! \left(x \right) F_{427}\! \left(x \right)\\
F_{427}\! \left(x \right) &= F_{428}\! \left(x \right)+F_{429}\! \left(x \right)\\
F_{428}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{421}\! \left(x \right)\\
F_{429}\! \left(x \right) &= F_{413}\! \left(x \right)+F_{430}\! \left(x \right)\\
F_{430}\! \left(x \right) &= F_{431}\! \left(x \right)\\
F_{431}\! \left(x \right) &= F_{23}\! \left(x \right) F_{413}\! \left(x \right)\\
F_{432}\! \left(x \right) &= F_{2}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{433}\! \left(x \right) &= F_{434}\! \left(x \right)\\
F_{434}\! \left(x \right) &= F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right) F_{435}\! \left(x \right)\\
F_{435}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{436}\! \left(x \right) &= -F_{442}\! \left(x \right)+F_{437}\! \left(x \right)\\
F_{437}\! \left(x \right) &= -F_{440}\! \left(x \right)+F_{438}\! \left(x \right)\\
F_{438}\! \left(x \right) &= \frac{F_{439}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{439}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{440}\! \left(x \right) &= F_{441}\! \left(x \right)\\
F_{441}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{442}\! \left(x \right) &= F_{443}\! \left(x \right)+F_{445}\! \left(x \right)\\
F_{443}\! \left(x \right) &= F_{444}\! \left(x \right)\\
F_{444}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{445}\! \left(x \right) &= -F_{468}\! \left(x \right)+F_{446}\! \left(x \right)\\
F_{446}\! \left(x \right) &= \frac{F_{447}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{447}\! \left(x \right) &= F_{448}\! \left(x \right)\\
F_{448}\! \left(x \right) &= F_{23}\! \left(x \right) F_{449}\! \left(x \right)\\
F_{449}\! \left(x \right) &= F_{450}\! \left(x \right)+F_{463}\! \left(x \right)\\
F_{450}\! \left(x \right) &= F_{451}\! \left(x \right)+F_{453}\! \left(x \right)\\
F_{451}\! \left(x \right) &= F_{20}\! \left(x \right) F_{21}\! \left(x \right) F_{452}\! \left(x \right)\\
F_{452}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{453}\! \left(x \right) &= F_{2}\! \left(x \right) F_{454}\! \left(x \right)\\
F_{454}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{455}\! \left(x \right)\\
F_{455}\! \left(x \right) &= F_{456}\! \left(x \right)+F_{458}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{456}\! \left(x \right) &= F_{23}\! \left(x \right) F_{457}\! \left(x \right)\\
F_{457}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{458}\! \left(x \right) &= F_{23}\! \left(x \right) F_{459}\! \left(x \right)\\
F_{459}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{460}\! \left(x \right)\\
F_{460}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{461}\! \left(x \right)\\
F_{461}\! \left(x \right) &= F_{462}\! \left(x \right)\\
F_{462}\! \left(x \right) &= F_{23}\! \left(x \right) F_{455}\! \left(x \right)\\
F_{463}\! \left(x \right) &= F_{464}\! \left(x \right) F_{466}\! \left(x \right)\\
F_{464}\! \left(x \right) &= F_{454}\! \left(x \right)+F_{465}\! \left(x \right)\\
F_{465}\! \left(x \right) &= F_{20}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{466}\! \left(x \right) &= F_{467}\! \left(x \right)\\
F_{467}\! \left(x \right) &= F_{23}\! \left(x \right) F_{452}\! \left(x \right)\\
F_{468}\! \left(x \right) &= F_{469}\! \left(x \right)\\
F_{469}\! \left(x \right) &= F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right) F_{470}\! \left(x \right)\\
F_{470}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{466}\! \left(x \right)\\
F_{471}\! \left(x \right) &= F_{472}\! \left(x \right)\\
F_{472}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{473}\! \left(x \right) F_{495}\! \left(x \right)\\
F_{473}\! \left(x \right) &= F_{474}\! \left(x \right)\\
F_{474}\! \left(x \right) &= F_{23}\! \left(x \right) F_{475}\! \left(x \right)\\
F_{475}\! \left(x \right) &= F_{476}\! \left(x \right)+F_{480}\! \left(x \right)\\
F_{476}\! \left(x \right) &= F_{477}\! \left(x \right)+F_{478}\! \left(x \right)\\
F_{477}\! \left(x \right) &= F_{23}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{478}\! \left(x \right) &= F_{479}\! \left(x \right)\\
F_{479}\! \left(x \right) &= F_{23}\! \left(x \right) F_{40}\! \left(x \right) F_{475}\! \left(x \right)\\
F_{480}\! \left(x \right) &= F_{481}\! \left(x \right)+F_{482}\! \left(x \right)\\
F_{481}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{473}\! \left(x \right)\\
F_{482}\! \left(x \right) &= F_{483}\! \left(x \right)+F_{484}\! \left(x \right)\\
F_{483}\! \left(x \right) &= F_{10}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{484}\! \left(x \right) &= F_{485}\! \left(x \right)\\
F_{485}\! \left(x \right) &= F_{23}\! \left(x \right) F_{486}\! \left(x \right)\\
F_{486}\! \left(x \right) &= F_{487}\! \left(x \right)+F_{491}\! \left(x \right)\\
F_{487}\! \left(x \right) &= F_{488}\! \left(x \right)+F_{490}\! \left(x \right)\\
F_{488}\! \left(x \right) &= F_{489}\! \left(x \right)\\
F_{489}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right) F_{481}\! \left(x \right)\\
F_{490}\! \left(x \right) &= F_{10}\! \left(x \right) F_{476}\! \left(x \right)\\
F_{491}\! \left(x \right) &= F_{492}\! \left(x \right)+F_{494}\! \left(x \right)\\
F_{492}\! \left(x \right) &= F_{493}\! \left(x \right)\\
F_{493}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right) F_{481}\! \left(x \right)\\
F_{494}\! \left(x \right) &= F_{10}\! \left(x \right) F_{480}\! \left(x \right)\\
F_{495}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{496}\! \left(x \right)\\
F_{496}\! \left(x \right) &= F_{497}\! \left(x \right)\\
F_{497}\! \left(x \right) &= F_{221}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{498}\! \left(x \right) &= F_{36}\! \left(x \right) F_{499}\! \left(x \right)\\
F_{499}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{500}\! \left(x \right)\\
F_{500}\! \left(x \right) &= F_{501}\! \left(x \right)\\
F_{501}\! \left(x \right) &= F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right) F_{495}\! \left(x \right)\\
F_{502}\! \left(x \right) &= F_{21}\! \left(x \right) F_{503}\! \left(x \right)\\
F_{503}\! \left(x \right) &= \frac{F_{504}\! \left(x \right)}{F_{23}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{504}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{505}\! \left(x \right) &= \frac{F_{506}\! \left(x \right)}{F_{23}\! \left(x \right)}\\
F_{506}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{507}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{508}\! \left(x \right)\\
F_{508}\! \left(x \right) &= F_{509}\! \left(x \right)\\
F_{509}\! \left(x \right) &= F_{2}\! \left(x \right) F_{21}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{510}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{511}\! \left(x \right)\\
F_{511}\! \left(x \right) &= F_{512}\! \left(x \right)\\
F_{512}\! \left(x \right) &= F_{21}\! \left(x \right) F_{23}\! \left(x \right) F_{513}\! \left(x \right)\\
F_{513}\! \left(x \right) &= F_{514}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{514}\! \left(x \right) &= F_{37}\! \left(x \right) F_{515}\! \left(x \right)\\
F_{515}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{516}\! \left(x \right) &= F_{517}\! \left(x \right)\\
F_{517}\! \left(x \right) &= F_{23}\! \left(x \right) F_{518}\! \left(x \right)\\
F_{518}\! \left(x \right) &= F_{519}\! \left(x \right)+F_{522}\! \left(x \right)\\
F_{519}\! \left(x \right) &= F_{4}\! \left(x \right) F_{520}\! \left(x \right)\\
F_{520}\! \left(x \right) &= F_{521}\! \left(x \right)\\
F_{521}\! \left(x \right) &= F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{522}\! \left(x \right) &= F_{523}\! \left(x \right)\\
F_{523}\! \left(x \right) &= F_{163}\! \left(x \right) F_{524}\! \left(x \right)\\
F_{524}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{481}\! \left(x \right)\\
F_{525}\! \left(x \right) &= F_{526}\! \left(x \right)\\
F_{526}\! \left(x \right) &= F_{23}\! \left(x \right) F_{35}\! \left(x \right) F_{527}\! \left(x \right)\\
F_{527}\! \left(x \right) &= F_{505}\! \left(x \right)+F_{528}\! \left(x \right)\\
F_{528}\! \left(x \right) &= F_{529}\! \left(x \right)\\
F_{529}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{530}\! \left(x \right) &= F_{531}\! \left(x \right)\\
F_{531}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{37}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Col Placements Req Corrob" and has 294 rules.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{8}\! \left(x \right) &= x\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{276}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{275}\! \left(x \right)\\
F_{17}\! \left(x \right) &= 0\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= \frac{F_{21}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{274}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32} \left(x \right)^{2} F_{2}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{33}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{260}\! \left(x \right)+F_{267}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{253}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{109}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{238}\! \left(x \right)+F_{244}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{237}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{8} \left(x \right)^{2}}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{51}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{225}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{214}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= -F_{15}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{74}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{20}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{36}\! \left(x \right) F_{8}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{33}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{85}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{69}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{8}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{92}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{8}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{101}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{2}\! \left(x \right) F_{32}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{102}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{121}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{104}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{103}\! \left(x \right) F_{109}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{110}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{103}\! \left(x \right) F_{36}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{105}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{103}\! \left(x \right) F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{115}\! \left(x \right) &= x^{2} F_{115} \left(x \right)^{3}+2 x^{2} F_{115} \left(x \right)^{2}+x^{2} F_{115}\! \left(x \right)+x F_{115} \left(x \right)^{2}+2 x F_{115}\! \left(x \right)+x\\
F_{116}\! \left(x \right) &= x^{2} F_{116} \left(x \right)^{3}-x^{2} F_{116} \left(x \right)^{2}+x F_{116} \left(x \right)^{2}+1\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{103}\! \left(x \right) F_{115}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{103}\! \left(x \right) F_{36}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{103}\! \left(x \right) F_{36}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{123}\! \left(x \right) &= 2 F_{17}\! \left(x \right)+F_{124}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{101}\! \left(x \right) F_{128}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{2}\! \left(x \right) F_{32}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{8}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{133}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{134}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{8}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{141}\! \left(x \right) &= 3 F_{17}\! \left(x \right)+F_{142}\! \left(x \right)+F_{208}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{202}\! \left(x \right)\\
F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{147}\! \left(x \right) &= -F_{201}\! \left(x \right)-3 F_{17}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{150}\! \left(x \right) &= \frac{F_{151}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{151}\! \left(x \right) &= -F_{0}\! \left(x \right)-F_{199}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{0}\! \left(x \right) F_{116}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{155}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{116}\! \left(x \right) F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{55}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{17}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{168}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{169}\! \left(x \right)+F_{182}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{109}\! \left(x \right) F_{171}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{173}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{168}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{176}\! \left(x \right)+F_{178}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{116}\! \left(x \right) F_{168}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{116}\! \left(x \right) F_{175}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{116} \left(x \right)^{2} F_{172}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{171}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{171}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{109}\! \left(x \right) F_{171}\! \left(x \right) F_{195}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{195}\! \left(x \right) &= \frac{F_{196}\! \left(x \right)}{F_{103}\! \left(x \right) F_{8}\! \left(x \right)}\\
F_{196}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{167}\! \left(x \right) F_{175}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{8}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{72}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{15}\! \left(x \right) F_{204}\! \left(x \right) F_{32}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{205}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{102}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{103}\! \left(x \right) F_{15}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{2}\! \left(x \right) F_{204}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{103}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{214}\! \left(x \right) &= -F_{222}\! \left(x \right)+F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= 3 F_{17}\! \left(x \right)+F_{216}\! \left(x \right)+F_{218}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= -F_{208}\! \left(x \right)-2 F_{17}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{218}\! \left(x \right) &= -F_{142}\! \left(x \right)-3 F_{17}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{103}\! \left(x \right) F_{51}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{103}\! \left(x \right) F_{224}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{103}\! \left(x \right) F_{227}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{227}\! \left(x \right) &= -F_{228}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{228}\! \left(x \right) &= \frac{F_{229}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= -F_{231}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{103}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{55}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{228}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{239}\! \left(x \right) &= \frac{F_{240}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{240}\! \left(x \right) &= -F_{17}\! \left(x \right)-F_{241}\! \left(x \right)-F_{242}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{53}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{247}\! \left(x \right) &= 2 F_{17}\! \left(x \right)+F_{248}\! \left(x \right)+F_{252}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{15}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{109}\! \left(x \right) F_{116}\! \left(x \right) F_{224}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{255}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= -F_{263}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= \frac{F_{258}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= -F_{2}\! \left(x \right)-F_{260}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{261}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{228}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{115}\! \left(x \right) F_{128}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{222}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{8}\! \left(x \right)}\\
F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= -F_{273}\! \left(x \right)+F_{243}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{26}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{72}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{280}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{109}\! \left(x \right) F_{247}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{282}\! \left(x \right)+F_{284}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{109}\! \left(x \right) F_{13}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{13}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{287}\! \left(x \right)+F_{292}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{289}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{116}\! \left(x \right) F_{128}\! \left(x \right) F_{172}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{116}\! \left(x \right) F_{154}\! \left(x \right) F_{8}\! \left(x \right)\\
\end{align*}\)