0123_0132_0231_1302
Counting sequence:
1, 1, 2, 6, 20, 66, 214, 688, 2206, 7070, 22660, 72634, 232830, 746352, 2392486, 7669286, 24584436, 78807122, 252621702, 809796400, 2595858574, 8321204878, 26674199972, 85506000010, 274095419758, 878631898608, 2816515554774, 9028536162646, 28941599524244, 92774306701794, 297394481489846, 953318658633648, 3055929149546494, 9795993063256318, 31401735903990724, 100660444675345370, 322674044301817054, 1034354052397630576, 3315693730576814982, 10628686463307929094, 34070992412092462900, 109216931739614070770, 350102457666654829926, 1122277735804345505840, 3597539202313600002798, 11532161691604200792814, 36967144985043185967844, 118500749893240924300714, 379862381337319122899918, 1217675237374081888265968, 3903342517082139278233270, 12512435449141399664904246, 40109480575628350929952212, 128573724802480514108364418, 412152001779569712691773590, 1321181857582998368420125872, 4235140174667925909691671902, 13576035877376919820284572766, 43518925594541111207261664004, 139502937529738820933082998266, 447186351996414005495721634366, 1433486899652062725776073839984, 4595141784404370874142649752422, 14730046032443071312263618419686, 47218185269993011345423839191412, 151361171260481041037844466028946, 485198743542226411020309929483590, 1555338259967736813218333741980976, 4985744780085023353100877067635534, 15982151054819864717057288862245198, 51231894853375107366453639805701156, 164227396003476577225270685263331530, 526442320263036593429407103125730350, 1687547408704347356035955278008135664, 5409550385694386935075009409213891990, 17340689348593649556840988512515431702, 55586783677924928662823697810112457236, 178187294492246644156531607099809832226, 571191744110133318370256104878323687286, 1830994793816639797406854065933399439792, 5869380938281252335068604023917970716862, 18814708111130316366976066077569352254910, 60311853162949374679027518484154564015684, 193333832789959668166579545973459237161498, 619745024253673983547609364788491646717342, 1986635704390449739288100076064861829518960, 6368298683336369484273553010698704569219398, 20414023582963395180541501980193456626333638, 65438569949024188469945039130335798465208244, 209767879397722654023028893833119614218583346, 672425501677297531547695203174021308341793574, 2155506632398525833457053915559612436039717424, 6909626167842437062543518730912391478680365486, 22149286419131694604708997058340755574490979758, 71001075450355516919568569837555487265851210084, 227598876989225470615053944703041713222540654058, 729584002470165513057125722885683177549708718734, 2338732175227671338658525280857345844254163855600, 7496968366804099984352962122899113831313020863094, 24032052617307462603383636540036880956984792201206, 77036413219819298481081548963319991342749470386772
Generating function in Maple syntax:
(x-1)*(x^2-3*x+1)/(4*x^3-7*x^2+5*x-1)
Generating function in latex syntax:
\frac{\left(x -1\right) \left(x^{2}-3 x +1\right)}{4 x^{3}-7 x^{2}+5 x -1}
Generating function in sympy syntax:
(x - 1)*(x**2 - 3*x + 1)/(4*x**3 - 7*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(4*x^3-7*x^2+5*x-1)*F(x)-(x-1)*(x^2-3*x+1) = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{3}-7 x^{2}+5 x -1\right) F \! \left(x \right)-\left(x -1\right) \left(x^{2}-3 x +1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/171336*(((1947*I+110*59^(1/2))*3^(1/2)-330*I*59^(1/2)-1947)*(71+6*59^(1/2)*3^(1/2))^(1/3)+42834+((-177*I+32*59^(1/2))*3^(1/2)+96*I*59^(1/2)-177)*(71+6*59^(1/2)*3^(1/2))^(2/3))*(1/2904*((71*I-6*59^(1/2))*3^(1/2)-18*I*59^(1/2)+71)*(71+6*59^(1/2)*3^(1/2))^(2/3)-1/24*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)+1/24*(71+6*59^(1/2)*3^(1/2))^(1/3)+7/12)^(-n)+1/171336*(((177*I+32*59^(1/2))*3^(1/2)-96*I*59^(1/2)-177)*(71+6*59^(1/2)*3^(1/2))^(2/3)+42834+((-1947*I+110*59^(1/2))*3^(1/2)+330*I*59^(1/2)-1947)*(71+6*59^(1/2)*3^(1/2))^(1/3))*(1/2904*((-71*I-6*59^(1/2))*3^(1/2)+18*I*59^(1/2)+71)*(71+6*59^(1/2)*3^(1/2))^(2/3)+1/24*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)+1/24*(71+6*59^(1/2)*3^(1/2))^(1/3)+7/12)^(-n)-5/3894*((16/55*59^(1/2)*3^(1/2)-177/110)*(71+6*59^(1/2)*3^(1/2))^(2/3)+(71+6*59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/2)-177/10*(71+6*59^(1/2)*3^(1/2))^(1/3)-1947/10)*(-1/12*(71+6*59^(1/2)*3^(1/2))^(1/3)+7/12-71/1452*(71+6*59^(1/2)*3^(1/2))^(2/3)+1/242*(71+6*59^(1/2)*3^(1/2))^(2/3)*59^(1/2)*3^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(\left(1947 \,\mathrm{I}+110 \sqrt{59}\right) \sqrt{3}-330 \,\mathrm{I} \sqrt{59}-1947\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+42834+\left(\left(-177 \,\mathrm{I}+32 \sqrt{59}\right) \sqrt{3}+96 \,\mathrm{I} \sqrt{59}-177\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(71 \,\mathrm{I}-6 \sqrt{59}\right) \sqrt{3}-18 \,\mathrm{I} \sqrt{59}+71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{2904}-\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{24}+\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{24}+\frac{7}{12}\right)^{-n}}{171336}\\+\\\frac{\left(\left(\left(177 \,\mathrm{I}+32 \sqrt{59}\right) \sqrt{3}-96 \,\mathrm{I} \sqrt{59}-177\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}+42834+\left(\left(-1947 \,\mathrm{I}+110 \sqrt{59}\right) \sqrt{3}+330 \,\mathrm{I} \sqrt{59}-1947\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-71 \,\mathrm{I}-6 \sqrt{59}\right) \sqrt{3}+18 \,\mathrm{I} \sqrt{59}+71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{2904}+\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{24}+\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{24}+\frac{7}{12}\right)^{-n}}{171336}\\-\\\frac{5 \left(\left(\frac{16 \sqrt{59}\, \sqrt{3}}{55}-\frac{177}{110}\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}+\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, \sqrt{3}-\frac{177 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{10}-\frac{1947}{10}\right) \left(-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{7}{12}-\frac{71 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{1452}+\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{59}\, \sqrt{3}}{242}\right)^{-n}}{3894} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 4*a(n)-7*a(n+1)+5*a(n+2), n >= 4
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(n +3\right) = 4 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right), \quad n \geq 4
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14795/
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[20,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[11,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = x
F[11,x] = F[12,x]+F[15,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = F[1,x]+F[12,x]
F[15,x] = F[16,x]+F[17,x]+F[19,x]
F[16,x] = 0
F[17,x] = F[10,x]*F[18,x]
F[18,x] = F[10,x]+F[15,x]
F[19,x] = F[10,x]*F[12,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[16,x]+F[22,x]+F[62,x]
F[22,x] = F[10,x]*F[23,x]
F[23,x] = F[24,x]+F[33,x]
F[24,x] = F[25,x]+F[6,x]
F[25,x] = F[26,x]
F[26,x] = F[10,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[10,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[32,x]
F[32,x] = F[10,x]+F[30,x]
F[33,x] = F[21,x]+F[34,x]
F[34,x] = 2*F[16,x]+F[35,x]+F[39,x]
F[35,x] = F[10,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[25,x]
F[38,x] = F[34,x]
F[39,x] = F[10,x]*F[40,x]
F[40,x] = F[41,x]+F[54,x]
F[41,x] = F[42,x]
F[42,x] = F[16,x]+F[43,x]+F[53,x]
F[43,x] = F[10,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[10,x]+F[46,x]
F[46,x] = F[26,x]
F[47,x] = F[42,x]+F[48,x]
F[48,x] = 2*F[16,x]+F[39,x]+F[49,x]
F[49,x] = F[10,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[46,x]
F[52,x] = F[48,x]
F[53,x] = F[10,x]*F[2,x]
F[54,x] = F[55,x]
F[55,x] = 2*F[16,x]+F[56,x]+F[60,x]
F[56,x] = F[10,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[30,x]
F[59,x] = F[55,x]
F[60,x] = F[10,x]*F[61,x]
F[61,x] = F[42,x]+F[55,x]
F[62,x] = F[10,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[2,x]+F[42,x]
F[65,x] = F[66,x]+F[79,x]
F[66,x] = F[16,x]+F[67,x]+F[77,x]
F[67,x] = F[10,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[12,x]+F[70,x]
F[70,x] = F[26,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = 2*F[16,x]+F[39,x]+F[73,x]
F[73,x] = F[10,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[70,x]
F[76,x] = F[72,x]
F[77,x] = F[10,x]*F[78,x]
F[78,x] = F[2,x]+F[66,x]
F[79,x] = F[16,x]+F[56,x]+F[80,x]+F[82,x]
F[80,x] = F[10,x]*F[81,x]
F[81,x] = F[42,x]+F[79,x]
F[82,x] = F[10,x]*F[66,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_{20}\! \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_{11}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = x
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{10}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)+F_{62}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \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_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \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_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{54}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right)+F_{43}\! \left(x \right)+F_{53}\! \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_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{10}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{26}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \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_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{10}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right)+F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{10}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{79}\! \left(x \right)
F_{66}\! \left(x \right) = F_{16}\! \left(x \right)+F_{67}\! \left(x \right)+F_{77}\! \left(x \right)
F_{67}\! \left(x \right) = F_{10}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{26}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{73}\! \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_{70}\! \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_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{79}\! \left(x \right) = F_{16}\! \left(x \right)+F_{56}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{10}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{42}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{10}\! \left(x \right) F_{66}\! \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_20(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_11(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), x)
Eq(F_11(x), F_12(x) + F_15(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), F_1(x) + F_12(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_19(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_10(x)*F_18(x))
Eq(F_18(x), F_10(x) + F_15(x))
Eq(F_19(x), F_10(x)*F_12(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_16(x) + F_22(x) + F_62(x))
Eq(F_22(x), F_10(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_33(x))
Eq(F_24(x), F_25(x) + F_6(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_10(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_10(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_32(x))
Eq(F_32(x), F_10(x) + F_30(x))
Eq(F_33(x), F_21(x) + F_34(x))
Eq(F_34(x), 2*F_16(x) + F_35(x) + F_39(x))
Eq(F_35(x), F_10(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_25(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_10(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_54(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_16(x) + F_43(x) + F_53(x))
Eq(F_43(x), F_10(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_10(x) + F_46(x))
Eq(F_46(x), F_26(x))
Eq(F_47(x), F_42(x) + F_48(x))
Eq(F_48(x), 2*F_16(x) + F_39(x) + F_49(x))
Eq(F_49(x), F_10(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_46(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_10(x)*F_2(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), 2*F_16(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_10(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_30(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_10(x)*F_61(x))
Eq(F_61(x), F_42(x) + F_55(x))
Eq(F_62(x), F_10(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_2(x) + F_42(x))
Eq(F_65(x), F_66(x) + F_79(x))
Eq(F_66(x), F_16(x) + F_67(x) + F_77(x))
Eq(F_67(x), F_10(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_12(x) + F_70(x))
Eq(F_70(x), F_26(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), 2*F_16(x) + F_39(x) + F_73(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_70(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_10(x)*F_78(x))
Eq(F_78(x), F_2(x) + F_66(x))
Eq(F_79(x), F_16(x) + F_56(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_10(x)*F_81(x))
Eq(F_81(x), F_42(x) + F_79(x))
Eq(F_82(x), F_10(x)*F_66(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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"comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 3, 0, 2], "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, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 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