0213_0231_0312_3120
Counting sequence:
1, 1, 2, 6, 20, 65, 198, 564, 1516, 3887, 9598, 23002, 53828, 123581, 279366, 623584, 1377420, 3016011, 6555166, 14157574, 30410756, 65014041, 138414662, 293604236, 620760300, 1308626535, 2751467518, 5771366834, 12079600516, 25232938357, 52613355398, 109521672632, 227633273868, 472446410371, 979252551966, 2027224572894, 4191888090820, 8658654079441, 17867063962886, 36833639542884, 75866302329836, 156130651158431, 321057395325822, 659706976681866, 1354598325437380, 2779565395036205, 5699868278410438, 11681211533513104, 23925373020427916, 48976645947677627, 100205091709018398, 204913783045383862, 418834765345483908, 855683929200423561, 1747396655419783366, 3566850904877465404, 7277816997830755820, 14843864371813190871, 30264189495929771006, 61681300496466352994, 125668444002146362116, 255948574022720072421, 521120520082294878982, 1060687784238299265896, 2158269056624017589260, 4390325089542873337075, 8928224131675423036958, 18151596168530198847374, 36893488147419103291716, 74967567915555617829697, 152296319072546058206598, 309315004627961761564692, 628074742221662813491948, 1275038950374804207771151, 2587856832612565577181566, 5251271528951045477709114, 10653658785353919602180420, 21609549025611496497958301, 43823560961030307583187526, 88856047741675244340995904, 180129947122579747031315596, 365095597523618010761364011, 739862601604153054920282142, 1499068016322140176635764326, 3036821658871948486862023940, 6151014570199233240905137145, 12456771645309139016172555078, 25223028300439623101069777644, 51065026620521936339588999916, 103367993280329252954077002567, 209211866639229266457952127998, 423375493435600054015500623122, 856654507185483150230194105988, 1733116054999532384858774061141, 3505846191256196938514319954566, 7090920545026658214622183712024, 14340297415081845104431455172620, 28997507480220747559237085989731, 58628840260555609819222523420446, 118525331121339449039941749879614, 239585963443135356882876905998276
Generating function in Maple syntax:
-(6*x^5-21*x^4+28*x^3-20*x^2+7*x-1)/(2*x-1)^2/(x-1)^4
Generating function in latex syntax:
-\frac{6 x^{5}-21 x^{4}+28 x^{3}-20 x^{2}+7 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-6*x**5 + 21*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^4*F(x)+6*x^5-21*x^4+28*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)+6 x^{5}-21 x^{4}+28 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
12+3/2*n^2+16/3*n+1/6*n^3+2^(n+1)*n-11*2^n
Explicit closed form in latex syntax:
12+\frac{3 n^{2}}{2}+\frac{16 n}{3}+\frac{n^{3}}{6}+2^{n +1} n -11 \,2^{n}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(n+2) = 1/6*n^3+1/2*n^2-4*a(n)+4*a(n+1)-2/3*n+2, n >= 6
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) = 20
a \! \left(5\right) = 65
a \! \left(n +2\right) = \frac{n^{3}}{6}+\frac{n^{2}}{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{2 n}{3}+2, \quad n \geq 6
Specification 1
Strategy pack name: row_placements
Tree: http://permpal.com/tree/21308/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[16,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[91,x]
F[4,x] = F[5,x]
F[5,x] = F[16,x]*F[6,x]
F[6,x] = F[34,x]+F[60,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[16,x]
F[10,x] = F[11,x]+F[7,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[30,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[17,x]
F[16,x] = x
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[18,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[16,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[26,x]+F[27,x]+F[29,x]
F[26,x] = 0
F[27,x] = F[16,x]*F[28,x]
F[28,x] = F[19,x]+F[25,x]
F[29,x] = F[16,x]*F[21,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[24,x]*F[31,x]
F[34,x] = F[13,x]*F[16,x]*F[35,x]
F[35,x] = F[36,x]+F[41,x]
F[36,x] = F[24,x]+F[37,x]
F[37,x] = F[19,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[22,x]+F[38,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[22,x]+F[43,x]
F[43,x] = F[26,x]+F[44,x]+F[46,x]
F[44,x] = F[16,x]*F[45,x]
F[45,x] = F[22,x]+F[43,x]
F[46,x] = F[16,x]*F[47,x]
F[47,x] = F[22,x]+F[48,x]
F[48,x] = F[46,x]
F[49,x] = F[50,x]+F[55,x]
F[50,x] = F[26,x]+F[51,x]+F[53,x]
F[51,x] = F[16,x]*F[52,x]
F[52,x] = F[19,x]+F[50,x]
F[53,x] = F[16,x]*F[54,x]
F[54,x] = F[22,x]+F[50,x]
F[55,x] = 2*F[26,x]+F[56,x]+F[58,x]
F[56,x] = F[16,x]*F[57,x]
F[57,x] = F[38,x]+F[55,x]
F[58,x] = F[16,x]*F[59,x]
F[59,x] = F[43,x]+F[55,x]
F[60,x] = F[13,x]*F[16,x]*F[61,x]
F[61,x] = F[62,x]+F[75,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]*F[66,x]
F[66,x] = F[63,x]+F[67,x]
F[67,x] = F[22,x]
F[68,x] = F[22,x]+F[69,x]
F[69,x] = F[26,x]+F[70,x]+F[72,x]
F[70,x] = F[16,x]*F[71,x]
F[71,x] = F[64,x]+F[69,x]
F[72,x] = F[16,x]*F[73,x]
F[73,x] = F[68,x]+F[74,x]
F[74,x] = F[48,x]
F[75,x] = F[76,x]+F[81,x]
F[76,x] = F[22,x]+F[77,x]
F[77,x] = F[26,x]+F[44,x]+F[78,x]
F[78,x] = F[16,x]*F[79,x]
F[79,x] = F[76,x]+F[80,x]
F[80,x] = F[48,x]
F[81,x] = F[48,x]+F[82,x]
F[82,x] = 2*F[26,x]+F[83,x]+F[85,x]
F[83,x] = F[16,x]*F[84,x]
F[84,x] = F[77,x]+F[82,x]
F[85,x] = F[16,x]*F[86,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[16,x]*F[90,x]
F[90,x] = F[48,x]+F[88,x]
F[91,x] = F[92,x]
F[92,x] = F[16,x]*F[93,x]
F[93,x] = F[3,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[16,x]*F[30,x]*F[96,x]
F[96,x] = F[1,x]+F[100,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[16,x]*F[99,x]
F[99,x] = F[24,x]+F[42,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_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{91}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{16}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{7}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{30}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right) F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{26}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{16}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{38}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{43}\! \left(x \right)+F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{75}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right)
F_{68}\! \left(x \right) = F_{22}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{26}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{48}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{81}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{26}\! \left(x \right)+F_{44}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{48}\! \left(x \right)
F_{81}\! \left(x \right) = F_{48}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{83}\! \left(x \right) = F_{16}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{16}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{16}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{48}\! \left(x \right)+F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{3}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{16}\! \left(x \right) F_{30}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{24}\! \left(x \right)+F_{42}\! \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_16(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_91(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_16(x)*F_6(x))
Eq(F_6(x), F_34(x) + F_60(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_16(x))
Eq(F_10(x), F_11(x) + F_7(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_30(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_17(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_18(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_16(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_29(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_19(x) + F_25(x))
Eq(F_29(x), F_16(x)*F_21(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_24(x)*F_31(x))
Eq(F_34(x), F_13(x)*F_16(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_41(x))
Eq(F_36(x), F_24(x) + F_37(x))
Eq(F_37(x), F_19(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_22(x) + F_38(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_22(x) + F_43(x))
Eq(F_43(x), F_26(x) + F_44(x) + F_46(x))
Eq(F_44(x), F_16(x)*F_45(x))
Eq(F_45(x), F_22(x) + F_43(x))
Eq(F_46(x), F_16(x)*F_47(x))
Eq(F_47(x), F_22(x) + F_48(x))
Eq(F_48(x), F_46(x))
Eq(F_49(x), F_50(x) + F_55(x))
Eq(F_50(x), F_26(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_16(x)*F_52(x))
Eq(F_52(x), F_19(x) + F_50(x))
Eq(F_53(x), F_16(x)*F_54(x))
Eq(F_54(x), F_22(x) + F_50(x))
Eq(F_55(x), 2*F_26(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_16(x)*F_57(x))
Eq(F_57(x), F_38(x) + F_55(x))
Eq(F_58(x), F_16(x)*F_59(x))
Eq(F_59(x), F_43(x) + F_55(x))
Eq(F_60(x), F_13(x)*F_16(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_75(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x)*F_66(x))
Eq(F_66(x), F_63(x) + F_67(x))
Eq(F_67(x), F_22(x))
Eq(F_68(x), F_22(x) + F_69(x))
Eq(F_69(x), F_26(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_16(x)*F_71(x))
Eq(F_71(x), F_64(x) + F_69(x))
Eq(F_72(x), F_16(x)*F_73(x))
Eq(F_73(x), F_68(x) + F_74(x))
Eq(F_74(x), F_48(x))
Eq(F_75(x), F_76(x) + F_81(x))
Eq(F_76(x), F_22(x) + F_77(x))
Eq(F_77(x), F_26(x) + F_44(x) + F_78(x))
Eq(F_78(x), F_16(x)*F_79(x))
Eq(F_79(x), F_76(x) + F_80(x))
Eq(F_80(x), F_48(x))
Eq(F_81(x), F_48(x) + F_82(x))
Eq(F_82(x), 2*F_26(x) + F_83(x) + F_85(x))
Eq(F_83(x), F_16(x)*F_84(x))
Eq(F_84(x), F_77(x) + F_82(x))
Eq(F_85(x), F_16(x)*F_86(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_16(x)*F_90(x))
Eq(F_90(x), F_48(x) + F_88(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_16(x)*F_93(x))
Eq(F_93(x), F_3(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_16(x)*F_30(x)*F_96(x))
Eq(F_96(x), F_1(x) + F_100(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_16(x)*F_99(x))
Eq(F_99(x), F_24(x) + F_42(x))
Eq(F_100(x), F_16(x)*F_96(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 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[0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], 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0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": 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3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 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]]}], "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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], 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