0231_0321_1230
Counting sequence:
1, 1, 2, 6, 21, 77, 286, 1066, 3977, 14841, 55386, 206702, 771421, 2878981, 10744502, 40099026, 149651601, 558507377, 2084377906, 7779004246, 29031639077, 108347552061, 404358569166, 1509086724602, 5631988329241, 21018866592361, 78443478040202, 292755045568446, 1092576704233581, 4077551771365877, 15217630381229926, 56792969753553826, 211954248632985377, 791024024778387681, 2952141850480565346, 11017543377143873702, 41118031658094929461, 153454583255235844141, 572700301362848447102, 2137346622196157944266, 7976686187421783329961, 29769398127490975375577, 111100906322542118172346, 414634227162677497313806, 1547436002328167871082877, 5775109782149993987017701, 21553003126271808076987926, 80436902722937238320934002, 300194607765477145206748081, 1120341528338971342506058321, 4181171505590408224817485202, 15604344494022661556763882486, 58236206470500238002238044741, 217340481387978290452188296477, 811125719081412923806515141166, 3027162394937673404773872268186, 11297523860669280695288973931577, 42162933047739449376382023458121, 157354208330288516810239119900906, 587253900273414617864574456145502, 2191661392763369954648058704681101, 8179391670780065200727660362578901, 30525905290356890848262582745634502, 113924229490647498192322670619959106, 425171012672233101921028099734201921, 1586759821198284909491789728316848577, 5921868272120906536046130813533192386, 22100713267285341234692733525815920966, 82480984797020458402724803289730491477, 307823225920796492376206479633106044941, 1148811918886165511102101115242693688286, 4287424449623865552032197981337668708202, 16000885879609296697026690810107981144521, 59716119068813321236074565259094255869881, 222863590395643988247271570226269042335002, 831738242513762631753011715645981913470126, 3104089379659406538764775292357658611545501, 11584619276123863523306089453784652532711877, 43234387724836047554459582522780951519302006, 161352931623220326694532240637339153544496146, 602177338768045259223669380026575662658682577, 2247356423448960710200145279468963497090234161, 8387248355027797581576911737849278325702254066, 31301636996662229616107501671928149805718782102, 116819299631621120882853094949863320897172874341, 435975561529822253915304878127525133782972715261, 1627082946487667894778366417560237214234717986702, 6072356224420849325198160792113423723155899231546, 22662341951195729406014276750893457678388878939481, 84577011580362068298858946211460406990399616526377, 315645704370252543789421508094948170283209587166026, 1178005805900648106858827086168332274142438732137726, 4396377519232339883645886836578380926286545341384877, 16407504271028711427724720260145191431003742633401781, 61233639564882505827252994204002384797728425192222246, 228527053988501311881287256555864347759909958135487202, 852874576389122741697896032019455006241911407349726561, 3182971251567989654910296871521955677207735671263419041, 11879010429882835877943291454068367702589031277703949602, 44333070467963353856862868944751515133148389439552379366, 165453271441970579549508184324937692830004526480505567861
Generating function in Maple syntax:
-(2*x^2-4*x+1)/(x-1)/(x^2-4*x+1)
Generating function in latex syntax:
-\frac{2 x^{2}-4 x +1}{\left(x -1\right) \left(x^{2}-4 x +1\right)}
Generating function in sympy syntax:
(-2*x**2 + 4*x - 1)/((x - 1)*(x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2-4*x+1)*F(x)+2*x^2-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}-4 x +1\right) F \! \left(x \right)+2 x^{2}-4 x +1 = 0
Explicit closed form in Maple syntax:
1/12*(-3^(1/2)+3)*(2-3^(1/2))^(-n)+1/2+1/12*(3^(1/2)+3)*(2+3^(1/2))^(-n)
Explicit closed form in latex syntax:
\frac{\left(-\sqrt{3}+3\right) \left(2-\sqrt{3}\right)^{-n}}{12}+\frac{1}{2}+\frac{\left(\sqrt{3}+3\right) \left(2+\sqrt{3}\right)^{-n}}{12}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+2) = -a(n)+4*a(n+1)-1, n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n +2\right) = -a \! \left(n \right)+4 a \! \left(n +1\right)-1, \quad n \geq 3
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14754/
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[10,x]*F[4,x]
F[4,x] = F[16,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[10,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = x
F[11,x] = F[12,x]+F[13,x]+F[14,x]
F[12,x] = 0
F[13,x] = F[10,x]*F[6,x]
F[14,x] = F[10,x]*F[15,x]
F[15,x] = F[9,x]
F[16,x] = F[17,x]+F[56,x]
F[17,x] = F[18,x]
F[18,x] = F[10,x]*F[19,x]
F[19,x] = F[20,x]+F[24,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[10,x]*F[23,x]
F[23,x] = F[1,x]+F[10,x]
F[24,x] = F[17,x]+F[25,x]
F[25,x] = F[12,x]+F[26,x]+F[54,x]
F[26,x] = F[10,x]*F[27,x]
F[27,x] = F[28,x]+F[32,x]
F[28,x] = F[21,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[10,x]*F[31,x]
F[31,x] = F[10,x]
F[32,x] = F[25,x]+F[33,x]
F[33,x] = 2*F[12,x]+F[34,x]+F[38,x]
F[34,x] = F[10,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[29,x]
F[37,x] = F[33,x]
F[38,x] = F[10,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]+F[41,x]+F[53,x]
F[41,x] = F[10,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[10,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = x^2
F[46,x] = F[40,x]+F[47,x]
F[47,x] = 2*F[12,x]+F[48,x]+F[52,x]
F[48,x] = F[10,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[44,x]
F[51,x] = F[47,x]
F[52,x] = F[10,x]*F[40,x]
F[53,x] = F[10,x]*F[17,x]
F[54,x] = F[10,x]*F[55,x]
F[55,x] = F[17,x]+F[40,x]
F[56,x] = F[12,x]+F[57,x]+F[99,x]
F[57,x] = F[10,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[6,x]+F[60,x]
F[60,x] = F[12,x]+F[14,x]+F[61,x]
F[61,x] = F[10,x]*F[62,x]
F[62,x] = F[11,x]+F[6,x]
F[63,x] = F[56,x]+F[64,x]
F[64,x] = F[12,x]+F[65,x]+F[94,x]+F[97,x]
F[65,x] = F[10,x]*F[66,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[60,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[10,x]*F[70,x]
F[70,x] = F[11,x]
F[71,x] = F[64,x]+F[72,x]
F[72,x] = 2*F[12,x]+F[73,x]+F[77,x]+F[92,x]
F[73,x] = F[10,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[68,x]
F[76,x] = F[72,x]
F[77,x] = F[10,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]+F[80,x]+F[93,x]+F[94,x]
F[80,x] = F[10,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[11,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[10,x]*F[11,x]
F[85,x] = F[79,x]+F[86,x]
F[86,x] = 2*F[12,x]+F[87,x]+F[91,x]+F[92,x]
F[87,x] = F[10,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[83,x]
F[90,x] = F[86,x]
F[91,x] = F[10,x]*F[79,x]
F[92,x] = 0
F[93,x] = F[10,x]*F[56,x]
F[94,x] = F[10,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[40,x]+F[79,x]
F[97,x] = F[10,x]*F[98,x]
F[98,x] = F[56,x]+F[79,x]
F[99,x] = F[10,x]*F[100,x]
F[100,x] = F[16,x]+F[96,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = x
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{9}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{56}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \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_{10}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)+F_{26}\! \left(x \right)+F_{54}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{10}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{29}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)+F_{41}\! \left(x \right)+F_{53}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = x^{2}
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{54}\! \left(x \right) = F_{10}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right)+F_{57}\! \left(x \right)+F_{99}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{10}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{63}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right)+F_{65}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{65}\! \left(x \right) = F_{10}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{60}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)+F_{92}\! \left(x \right)
F_{73}\! \left(x \right) = F_{10}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{68}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{10}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right)+F_{80}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{80}\! \left(x \right) = F_{10}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{85}\! \left(x \right) = F_{79}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{87}\! \left(x \right) = F_{10}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right) F_{79}\! \left(x \right)
F_{92}\! \left(x \right) = 0
F_{93}\! \left(x \right) = F_{10}\! \left(x \right) F_{56}\! \left(x \right)
F_{94}\! \left(x \right) = F_{10}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{40}\! \left(x \right)+F_{79}\! \left(x \right)
F_{97}\! \left(x \right) = F_{10}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{56}\! \left(x \right)+F_{79}\! \left(x \right)
F_{99}\! \left(x \right) = F_{10}\! \left(x \right) F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{16}\! \left(x \right)+F_{96}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_16(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_10(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), x)
Eq(F_11(x), F_12(x) + F_13(x) + F_14(x))
Eq(F_12(x), 0)
Eq(F_13(x), F_10(x)*F_6(x))
Eq(F_14(x), F_10(x)*F_15(x))
Eq(F_15(x), F_9(x))
Eq(F_16(x), F_17(x) + F_56(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_10(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_24(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_10(x)*F_23(x))
Eq(F_23(x), F_1(x) + F_10(x))
Eq(F_24(x), F_17(x) + F_25(x))
Eq(F_25(x), F_12(x) + F_26(x) + F_54(x))
Eq(F_26(x), F_10(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_32(x))
Eq(F_28(x), F_21(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_10(x)*F_31(x))
Eq(F_31(x), F_10(x))
Eq(F_32(x), F_25(x) + F_33(x))
Eq(F_33(x), 2*F_12(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_10(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_29(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_10(x)*F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x) + F_41(x) + F_53(x))
Eq(F_41(x), F_10(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_10(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), x**2)
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), 2*F_12(x) + F_48(x) + F_52(x))
Eq(F_48(x), F_10(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_44(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_10(x)*F_40(x))
Eq(F_53(x), F_10(x)*F_17(x))
Eq(F_54(x), F_10(x)*F_55(x))
Eq(F_55(x), F_17(x) + F_40(x))
Eq(F_56(x), F_12(x) + F_57(x) + F_99(x))
Eq(F_57(x), F_10(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_6(x) + F_60(x))
Eq(F_60(x), F_12(x) + F_14(x) + F_61(x))
Eq(F_61(x), F_10(x)*F_62(x))
Eq(F_62(x), F_11(x) + F_6(x))
Eq(F_63(x), F_56(x) + F_64(x))
Eq(F_64(x), F_12(x) + F_65(x) + F_94(x) + F_97(x))
Eq(F_65(x), F_10(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_60(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_10(x)*F_70(x))
Eq(F_70(x), F_11(x))
Eq(F_71(x), F_64(x) + F_72(x))
Eq(F_72(x), 2*F_12(x) + F_73(x) + F_77(x) + F_92(x))
Eq(F_73(x), F_10(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_68(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_10(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x) + F_80(x) + F_93(x) + F_94(x))
Eq(F_80(x), F_10(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_11(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_10(x)*F_11(x))
Eq(F_85(x), F_79(x) + F_86(x))
Eq(F_86(x), 2*F_12(x) + F_87(x) + F_91(x) + F_92(x))
Eq(F_87(x), F_10(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_83(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_10(x)*F_79(x))
Eq(F_92(x), 0)
Eq(F_93(x), F_10(x)*F_56(x))
Eq(F_94(x), F_10(x)*F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_40(x) + F_79(x))
Eq(F_97(x), F_10(x)*F_98(x))
Eq(F_98(x), F_56(x) + F_79(x))
Eq(F_99(x), F_10(x)*F_100(x))
Eq(F_100(x), F_16(x) + F_96(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:
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"pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 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