Av(13452, 13542, 14253, 14352, 14532, 15243, 15342, 15432, 24153, 25143)
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Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2772, 14704, 79974, 443592, 2499596, 14268740, 82339972, 479549860, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(4 x -1\right) F \left(x \right)^{4}+\left(-16 x +6\right) F \left(x \right)^{3}+\left(x^{2}+24 x -13\right) F \left(x \right)^{2}+\left(-16 x +12\right) F \! \left(x \right)+4 x -4 = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 110\)
\(\displaystyle a(6) = 540\)
\(\displaystyle a(7) = 2772\)
\(\displaystyle a(8) = 14704\)
\(\displaystyle a(9) = 79974\)
\(\displaystyle a(10) = 443592\)
\(\displaystyle a(11) = 2499596\)
\(\displaystyle a(12) = 14268740\)
\(\displaystyle a(13) = 82339972\)
\(\displaystyle a(14) = 479549860\)
\(\displaystyle a(15) = 2815097792\)
\(\displaystyle a(16) = 16639456452\)
\(\displaystyle a(17) = 98947148126\)
\(\displaystyle a(18) = 591537712636\)
\(\displaystyle a(19) = 3553227623724\)
\(\displaystyle a{\left(n + 20 \right)} = \frac{4096 n \left(2 n - 1\right) \left(2 n + 1\right) a{\left(n \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{54 \left(n + 18\right)^{2} a{\left(n + 19 \right)}}{\left(n + 20\right) \left(2 n + 39\right)} + \frac{512 \left(2 n + 1\right) \left(916 n^{2} + 712 n - 9\right) a{\left(n + 1 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(26 n^{3} + 1479 n^{2} + 27763 n + 172098\right) a{\left(n + 18 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(2408 n^{3} + 118971 n^{2} + 1960519 n + 10776756\right) a{\left(n + 17 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{\left(10922 n^{3} + 528819 n^{2} + 8543575 n + 46047480\right) a{\left(n + 16 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{192 \left(42060 n^{3} + 208560 n^{2} + 343911 n + 187897\right) a{\left(n + 2 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(66845 n^{3} + 3002127 n^{2} + 44958874 n + 224503194\right) a{\left(n + 15 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(380062 n^{3} + 16360809 n^{2} + 231992765 n + 1085753814\right) a{\left(n + 13 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(396430 n^{3} + 17215119 n^{2} + 249931679 n + 1212253350\right) a{\left(n + 14 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{48 \left(432732 n^{3} + 4881254 n^{2} + 16662860 n + 17918773\right) a{\left(n + 3 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{3 \left(1791558 n^{3} + 66969187 n^{2} + 838710563 n + 3515080212\right) a{\left(n + 12 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(3022790 n^{3} + 79415085 n^{2} + 716407897 n + 2221131150\right) a{\left(n + 10 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(7589803 n^{3} + 252562797 n^{2} + 2822211764 n + 10582254672\right) a{\left(n + 11 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{4 \left(25400764 n^{3} + 306795900 n^{2} + 1230413339 n + 1639326000\right) a{\left(n + 4 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(44453726 n^{3} + 552325239 n^{2} + 2292850891 n + 3192582486\right) a{\left(n + 5 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(53441668 n^{3} + 1423814331 n^{2} + 12690543599 n + 37831782912\right) a{\left(n + 9 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(112014674 n^{3} + 2635668285 n^{2} + 19272760981 n + 44971622922\right) a{\left(n + 6 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(149062195 n^{3} + 3422417985 n^{2} + 25922787338 n + 64899906954\right) a{\left(n + 7 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(257312554 n^{3} + 6336497943 n^{2} + 51982150787 n + 142075461456\right) a{\left(n + 8 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)}, \quad n \geq 20\)
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 85 rules.

Finding the specification took 22744 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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= x\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{15}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{8}\! \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_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{11}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{40}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{11}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{14}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{11}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{73}\! \left(x \right) F_{9}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 86 rules.

Finding the specification took 7537 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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= x\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{15}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{11}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{11}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{35}\! \left(x \right) &= F_{23}\! \left(x \right)\\ F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= -F_{41}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{41}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{11}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{14}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{11}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{74}\! \left(x \right) F_{9}\! \left(x \right)\\ \end{align*}\)