Av(1234, 1342, 2431, 4132)
Generating Function
\(\displaystyle \frac{8 x^{12}-63 x^{11}+184 x^{10}-243 x^{9}+121 x^{8}+79 x^{7}-251 x^{6}+351 x^{5}-315 x^{4}+179 x^{3}-62 x^{2}+12 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4}}\)
Counting Sequence
1, 1, 2, 6, 20, 61, 164, 419, 1052, 2631, 6584, 16504, 41445, 104271, 262871, ...
Implicit Equation for the Generating Function
\(\displaystyle -\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4} F \! \left(x \right)+8 x^{12}-63 x^{11}+184 x^{10}-243 x^{9}+121 x^{8}+79 x^{7}-251 x^{6}+351 x^{5}-315 x^{4}+179 x^{3}-62 x^{2}+12 x -1 = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 20\)
\(\displaystyle a \! \left(5\right) = 61\)
\(\displaystyle a \! \left(6\right) = 164\)
\(\displaystyle a \! \left(7\right) = 419\)
\(\displaystyle a \! \left(8\right) = 1052\)
\(\displaystyle a \! \left(9\right) = 2631\)
\(\displaystyle a \! \left(10\right) = 6584\)
\(\displaystyle a \! \left(11\right) = 16504\)
\(\displaystyle a \! \left(12\right) = 41445\)
\(\displaystyle a \! \left(n +5\right) = \frac{n^{3}}{6}-n^{2}+8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)-\frac{37 n}{6}+18, \quad n \geq 13\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 20\)
\(\displaystyle a \! \left(5\right) = 61\)
\(\displaystyle a \! \left(6\right) = 164\)
\(\displaystyle a \! \left(7\right) = 419\)
\(\displaystyle a \! \left(8\right) = 1052\)
\(\displaystyle a \! \left(9\right) = 2631\)
\(\displaystyle a \! \left(10\right) = 6584\)
\(\displaystyle a \! \left(11\right) = 16504\)
\(\displaystyle a \! \left(12\right) = 41445\)
\(\displaystyle a \! \left(n +5\right) = \frac{n^{3}}{6}-n^{2}+8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)-\frac{37 n}{6}+18, \quad n \geq 13\)
Explicit Closed Form
\(\displaystyle \left(\left\{\begin{array}{cc}-\frac{47}{8} & n =0 \\ -\frac{31}{16} & n =1 \\ \frac{5}{8} & n =2 \\ 1 & n =3 \\ 0 & \text{otherwise} \end{array}\right.\right)+\frac{\left(-96 \sqrt{5}+480\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(96 \sqrt{5}+480\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(15 n^{2}+75 n -120\right) 2^{n}}{960}+\frac{n^{3}}{6}-\frac{25 n}{6}+6\)
This specification was found using the strategy pack "Point Placements" and has 190 rules.
Found on January 18, 2022.Finding the specification took 5 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{17}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{38}\! \left(x \right) &= 0\\
F_{39}\! \left(x \right) &= F_{4}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{4}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{4}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{53}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{4}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{50}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{4}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{38}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{7}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{4}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{4}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{175}\! \left(x \right)+F_{38}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{4}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{4}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{130}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{4}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{4}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{101}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{104}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{105}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{125}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{124}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{172}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{38}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{147}\! \left(x \right)+F_{161}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{151}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{155}\! \left(x \right)+F_{159}\! \left(x \right)+F_{98}\! \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_{158}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{150}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{154}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= 2 F_{38}\! \left(x \right)+F_{128}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{167}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{179}\! \left(x \right)\\
\end{align*}\)