0132_0231_1023_1302_3021
Counting sequence:
1, 1, 2, 6, 19, 55, 150, 397, 1038, 2706, 7058, 18432, 48185, 126050, 329869, 863435, 2260285, 5917237, 15491208, 40556131, 106176888, 277974192, 727745300, 1905261270, 4988038019, 13058852240, 34188518095, 89506701377, 234331585303, 613488053731, 1606132575018, 4204909670377, 11008596435090, 28820879633790, 75454042465094, 197541247760220, 517169700814205, 1353967854680942, 3544733863227073, 9280233734998631, 24295967341767073, 63607668290300737, 166527037529133180, 435973444297096735, 1141393295362154844, 2988206441789365500, 7823226030005939240, 20481471648228449682, 53621188914679407143, 140382095095809768956, 367525096372749896803, 962193194022439918397, 2519054485694569855195, 6594970263061269643855, 17265856303489239072894, 45202598647406447571205, 118341939638730103636950, 309823220268783863335722, 811127721167621486366138, 2123559943234080595758456, 5559552108534620300904833, 14555096382369780306951482, 38105737038574720619944885, 99762114733354381552878275, 261180607161488424038684869, 683779706751110890563171085, 1790158513091844247650822960, 4686695832524421852389292187, 12269928984481421309517047808, 32123091120919842076161845256, 84099344378278104918968481788, 220174942013914472680743593742, 576425481663465313123262292875, 1509101502976481466689043278120, 3950879027265979086943867534519, 10343535578821455794142559318265, 27079727709198388295483810412895, 70895647548773709092308871912827, 185607214937122738981442805317778, 485925997262594507852019544032481, 1272170776850660784574615826771418, 3330586333289387845871827936273302, 8719588223017502753040867982039790, 22828178335763120413250776009837140, 59764946784271858486711460047462469, 156466662017052455046883604132540870, 409635039266885506653939352350150505, 1072438455783604064914934452917900767, 2807680328083926688090864006403541673, 7350602528468175999357657566292713881, 19244127257320601309982108692474589348, 50381779243493627930588668511131043287, 131901210473160282481783896840918529380, 345321852175987219514763022011624533460, 904064346054801376062505169193955059344, 2366871185988416908672752485570240632650, 6196549211910449349955752287516766826415, 16222776449742931141194504376980059834132, 42471780137318344073627760843423412663243, 111192563962212101079688778153290178142581, 291105911749317959165438573616447121751203
Generating function in Maple syntax:
(x^8+x^7+2*x^5-2*x^4+6*x^3-9*x^2+5*x-1)/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{x^{8}+x^{7}+2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**8 + x**7 + 2*x**5 - 2*x**4 + 6*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x-1)^3*F(x)+x^8+x^7+2*x^5-2*x^4+6*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{8}+x^{7}+2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,98,n = 1,29,n = 2,7,n = 3,1,0)+1/2*(59*5^(1/2)-131)*(3/2-1/2*5^(1/2))^(-n)+1/2*(-59*5^(1/2)-131)*(3/2+1/2*5^(1/2))^(-n)+3/2*n^2-29/2*n+34
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}98 & n =0 \\ 29 & n =1 \\ 7 & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(59 \sqrt{5}-131\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{2}+\frac{\left(-59 \sqrt{5}-131\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{2}+\frac{3 n^{2}}{2}-\frac{29 n}{2}+34
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 150
a(7) = 397
a(8) = 1038
a(n+2) = -3/2*n^2-a(n)+3*a(n+1)+23/2*n-18, n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 150
a \! \left(7\right) = 397
a \! \left(8\right) = 1038
a \! \left(n +2\right) = -\frac{3 n^{2}}{2}-a \! \left(n \right)+3 a \! \left(n +1\right)+\frac{23 n}{2}-18, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18786/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[21,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]+F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[15,x]
F[21,x] = F[22,x]+F[36,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[35,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[17,x]+F[30,x]
F[30,x] = F[31,x]+F[33,x]
F[31,x] = F[27,x]+F[28,x]+F[32,x]
F[32,x] = F[22,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[30,x]*F[4,x]
F[35,x] = F[25,x]*F[4,x]
F[36,x] = F[27,x]+F[37,x]+F[90,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[47,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[1,x]+F[40,x]
F[43,x] = F[19,x]+F[27,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[11,x]+F[46,x]
F[46,x] = F[44,x]
F[47,x] = F[48,x]+F[52,x]
F[48,x] = F[27,x]+F[37,x]+F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[22,x]+F[51,x]
F[51,x] = F[49,x]
F[52,x] = F[27,x]+F[53,x]+F[65,x]+F[87,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[59,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[4,x]+F[56,x]
F[59,x] = F[60,x]
F[60,x] = 2*F[27,x]+F[53,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[32,x]
F[64,x] = F[61,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[86,x]
F[67,x] = F[27,x]+F[32,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[4,x]+F[71,x]
F[71,x] = F[19,x]+F[27,x]+F[72,x]
F[72,x] = F[11,x]*F[4,x]
F[73,x] = F[67,x]+F[74,x]
F[74,x] = F[27,x]+F[65,x]+F[75,x]+F[82,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[78,x]
F[78,x] = x^2
F[79,x] = F[80,x]
F[80,x] = 2*F[27,x]+F[75,x]+F[81,x]
F[81,x] = F[4,x]*F[63,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[22,x]+F[83,x]
F[86,x] = F[65,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[83,x]+F[89,x]
F[89,x] = F[87,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[95,x]
F[92,x] = F[22,x]+F[93,x]
F[93,x] = F[27,x]+F[68,x]+F[94,x]
F[94,x] = F[4,x]*F[92,x]
F[95,x] = F[107,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[85,x]+F[99,x]
F[99,x] = F[100,x]+F[96,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[106,x]
F[103,x] = F[104,x]+F[63,x]
F[104,x] = F[105,x]
F[105,x] = F[103,x]*F[4,x]
F[106,x] = F[101,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[111,x]+F[67,x]
F[111,x] = F[112,x]
F[112,x] = F[110,x]*F[4,x]
F[113,x] = F[108,x]
System of equations in latex syntax:
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_{21}\! \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_{7}\! \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_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{17}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{90}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{47}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{27}\! \left(x \right)+F_{53}\! \left(x \right)+F_{65}\! \left(x \right)+F_{87}\! \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_{59}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{32}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{86}\! \left(x \right)
F_{67}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \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_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{27}\! \left(x \right)+F_{65}\! \left(x \right)+F_{75}\! \left(x \right)+F_{82}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = x^{2}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \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_{22}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{65}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{83}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{22}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{27}\! \left(x \right)+F_{68}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{107}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{85}\! \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_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{106}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{63}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{101}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{67}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_21(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x) + F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_22(x) + F_36(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_35(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_17(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_33(x))
Eq(F_31(x), F_27(x) + F_28(x) + F_32(x))
Eq(F_32(x), F_22(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_30(x)*F_4(x))
Eq(F_35(x), F_25(x)*F_4(x))
Eq(F_36(x), F_27(x) + F_37(x) + F_90(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_47(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_40(x))
Eq(F_43(x), F_19(x) + F_27(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_11(x) + F_46(x))
Eq(F_46(x), F_44(x))
Eq(F_47(x), F_48(x) + F_52(x))
Eq(F_48(x), F_27(x) + F_37(x) + F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_22(x) + F_51(x))
Eq(F_51(x), F_49(x))
Eq(F_52(x), F_27(x) + F_53(x) + F_65(x) + F_87(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_59(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_4(x) + F_56(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), 2*F_27(x) + F_53(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_32(x))
Eq(F_64(x), F_61(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_86(x))
Eq(F_67(x), F_27(x) + F_32(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_4(x) + F_71(x))
Eq(F_71(x), F_19(x) + F_27(x) + F_72(x))
Eq(F_72(x), F_11(x)*F_4(x))
Eq(F_73(x), F_67(x) + F_74(x))
Eq(F_74(x), F_27(x) + F_65(x) + F_75(x) + F_82(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), x**2)
Eq(F_79(x), F_80(x))
Eq(F_80(x), 2*F_27(x) + F_75(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_63(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_22(x) + F_83(x))
Eq(F_86(x), F_65(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_83(x) + F_89(x))
Eq(F_89(x), F_87(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_95(x))
Eq(F_92(x), F_22(x) + F_93(x))
Eq(F_93(x), F_27(x) + F_68(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_92(x))
Eq(F_95(x), F_107(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_85(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_96(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_106(x))
Eq(F_103(x), F_104(x) + F_63(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_103(x)*F_4(x))
Eq(F_106(x), F_101(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x) + F_67(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_110(x)*F_4(x))
Eq(F_113(x), F_108(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, 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