0132_1203_2301
Counting sequence:
1, 1, 2, 6, 21, 73, 238, 722, 2054, 5541, 14323, 35788, 87043, 207201, 484772, 1118334, 2550164, 5759101, 12899521, 28689880, 63419177, 139435017, 305102778, 664755562, 1442788402, 3120497429, 6727583999, 14461863108, 31004177695, 66303416497, 141465316864, 301184381814, 639949891424, 1357209389037, 2873332798253, 6073083381520, 12816181977445, 27006753857497, 56831006687222, 119434449911586, 250688650386078, 525566557228933, 1100611138443979, 2302377347479868, 4811462881929083, 10045138229993985, 20952293577368860, 43663805760531694, 90916417475638636, 189151184347445853, 393220542462441305, 816840382411728840, 1695605259702126305, 3517311308973199273, 7291327796709358834, 15105073150196828506, 31272995812456542026, 64707719446054709493, 133810952128427176023, 276557045917561962292, 571272605532686733079, 1179438699212797991249, 2433817296225046943480, 5019820231058204115174, 10348623425351050203064, 21324436149208232737741, 43921697639502432746821, 90425939449324211604480, 186090754215581945470877, 382806833017620603039609, 787159463113333973545646, 1618000816193212177358866, 3324546003940230215429686, 6828541934229506962903909, 14020706087639976622212515, 28778101346607617913797292, 59048470501802043732305907, 121119255552640660419773089, 248358698067080381056171924, 509108885785210711174107998, 1043302982327424977745818180, 2137380849078664380853243965, 4377520392824572241582039281, 8962976026622860701240727480, 18346658238471612355308136345, 37544400253951923649640186697, 76810310875035079244094659882, 157102328110560290511377819466, 321245440194556181336281240418, 656727190840894235833941463765, 1342236487595173563059328947887, 2742656157036759999038960553892, 5602916617805631124193384279567, 11443517723154055261167449448945, 23367356181550838068995810925296, 47705257353901414273512589985878, 97371411730030870902465450531088, 198704231585774958684608159546285, 405410507585490615466164322360925, 826983560323891155801411678334704, 1686609123603659218691363535559381
Generating function in Maple syntax:
-(17*x^8-80*x^7+192*x^6-274*x^5+248*x^4-145*x^3+53*x^2-11*x+1)/(2*x-1)^3/(-1+x)^6
Generating function in latex syntax:
-\frac{17 x^{8}-80 x^{7}+192 x^{6}-274 x^{5}+248 x^{4}-145 x^{3}+53 x^{2}-11 x +1}{\left(2 x -1\right)^{3} \left(-1+x \right)^{6}}
Generating function in sympy syntax:
(-17*x**8 + 80*x**7 - 192*x**6 + 274*x**5 - 248*x**4 + 145*x**3 - 53*x**2 + 11*x - 1)/((x - 1)**6*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(-1+x)^6*F(x)+17*x^8-80*x^7+192*x^6-274*x^5+248*x^4-145*x^3+53*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(-1+x \right)^{6} F \! \left(x \right)+17 x^{8}-80 x^{7}+192 x^{6}-274 x^{5}+248 x^{4}-145 x^{3}+53 x^{2}-11 x +1 = 0
Explicit closed form in Maple syntax:
1/120*(15*n^2+105*n-840)*2^n-1/120*n^5+1/24*n^4-1/24*n^3+35/24*n^2+71/20*n+8
Explicit closed form in latex syntax:
\frac{\left(15 n^{2}+105 n -840\right) 2^{n}}{120}-\frac{n^{5}}{120}+\frac{n^{4}}{24}-\frac{n^{3}}{24}+\frac{35 n^{2}}{24}+\frac{71 n}{20}+8
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 238
a(7) = 722
a(8) = 2054
a(n+3) = 1/120*n^5-1/6*n^4+19/24*n^3-11/6*n^2+8*a(n)-12*a(n+1)+6*a(n+2)+21/5*n-2, 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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 238
a \! \left(7\right) = 722
a \! \left(8\right) = 2054
a \! \left(n +3\right) = \frac{n^{5}}{120}-\frac{n^{4}}{6}+\frac{19 n^{3}}{24}-\frac{11 n^{2}}{6}+8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)+\frac{21 n}{5}-2, \quad n \geq 9
Specification 1
Strategy pack name: point_and_row_placements
Tree: http://permpal.com/tree/290/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]+F[86,x]
F[6,x] = 0
F[7,x] = F[17,x]*F[8,x]
F[8,x] = F[41,x]+F[9,x]
F[9,x] = F[10,x]+F[32,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[17,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = x
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]+F[24,x]+F[6,x]
F[20,x] = F[17,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[15,x]
F[23,x] = F[19,x]
F[24,x] = F[17,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]
F[27,x] = F[17,x]*F[28,x]
F[28,x] = F[1,x]+F[26,x]
F[29,x] = F[24,x]+F[30,x]+F[6,x]
F[30,x] = F[17,x]*F[31,x]
F[31,x] = F[15,x]+F[29,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]
F[34,x] = F[17,x]*F[35,x]
F[35,x] = F[14,x]+F[25,x]
F[36,x] = F[37,x]
F[37,x] = F[17,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[33,x]
F[40,x] = F[36,x]
F[41,x] = F[42,x]+F[65,x]
F[42,x] = F[26,x]+F[43,x]
F[43,x] = F[44,x]+F[46,x]+F[6,x]
F[44,x] = F[17,x]*F[45,x]
F[45,x] = F[11,x]+F[43,x]
F[46,x] = F[17,x]*F[47,x]
F[47,x] = F[48,x]+F[52,x]
F[48,x] = F[26,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[17,x]*F[51,x]
F[51,x] = F[15,x]+F[49,x]
F[52,x] = F[43,x]+F[53,x]
F[53,x] = 2*F[6,x]+F[54,x]+F[61,x]
F[54,x] = F[17,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[57,x]
F[57,x] = F[17,x]*F[58,x]
F[58,x] = F[26,x]+F[59,x]
F[59,x] = F[57,x]
F[60,x] = F[54,x]
F[61,x] = F[17,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[49,x]
F[64,x] = F[53,x]
F[65,x] = F[66,x]+F[79,x]
F[66,x] = F[6,x]+F[67,x]+F[69,x]
F[67,x] = F[17,x]*F[68,x]
F[68,x] = F[33,x]+F[66,x]
F[69,x] = F[17,x]*F[70,x]
F[70,x] = F[25,x]+F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[17,x]*F[74,x]
F[74,x] = F[26,x]+F[72,x]
F[75,x] = 2*F[6,x]+F[76,x]+F[78,x]
F[76,x] = F[17,x]*F[77,x]
F[77,x] = F[29,x]+F[75,x]
F[78,x] = F[17,x]*F[71,x]
F[79,x] = 2*F[6,x]+F[80,x]+F[82,x]
F[80,x] = F[17,x]*F[81,x]
F[81,x] = F[36,x]+F[79,x]
F[82,x] = F[17,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[66,x]
F[85,x] = F[79,x]
F[86,x] = F[17,x]*F[87,x]
F[87,x] = F[5,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[11,x]*F[17,x]*F[28,x]*F[90,x]
F[90,x] = F[28,x]+F[91,x]
F[91,x] = F[26,x]+F[92,x]
F[92,x] = F[6,x]+F[93,x]+F[95,x]
F[93,x] = F[17,x]*F[94,x]
F[94,x] = F[26,x]+F[92,x]
F[95,x] = F[17,x]*F[91,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)+F_{86}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{41}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \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_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{17}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{65}\! \left(x \right)
F_{42}\! \left(x \right) = F_{26}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)+F_{6}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{26}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{6}\! \left(x \right)+F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{26}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{17}\! \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_{49}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{79}\! \left(x \right)
F_{66}\! \left(x \right) = F_{6}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{17}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{33}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{17}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{25}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{26}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{6}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{17}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{17}\! \left(x \right) F_{71}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{6}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{17}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{36}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{17}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{66}\! \left(x \right)
F_{85}\! \left(x \right) = F_{79}\! \left(x \right)
F_{86}\! \left(x \right) = F_{17}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{5}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{28}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{28}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{26}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{6}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{17}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{26}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{17}\! \left(x \right) F_{91}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x) + F_86(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_17(x)*F_8(x))
Eq(F_8(x), F_41(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_32(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_17(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_24(x) + F_6(x))
Eq(F_20(x), F_17(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_15(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_17(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_28(x))
Eq(F_28(x), F_1(x) + F_26(x))
Eq(F_29(x), F_24(x) + F_30(x) + F_6(x))
Eq(F_30(x), F_17(x)*F_31(x))
Eq(F_31(x), F_15(x) + F_29(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_17(x)*F_35(x))
Eq(F_35(x), F_14(x) + F_25(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_17(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_33(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_42(x) + F_65(x))
Eq(F_42(x), F_26(x) + F_43(x))
Eq(F_43(x), F_44(x) + F_46(x) + F_6(x))
Eq(F_44(x), F_17(x)*F_45(x))
Eq(F_45(x), F_11(x) + F_43(x))
Eq(F_46(x), F_17(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_52(x))
Eq(F_48(x), F_26(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_17(x)*F_51(x))
Eq(F_51(x), F_15(x) + F_49(x))
Eq(F_52(x), F_43(x) + F_53(x))
Eq(F_53(x), F_54(x) + 2*F_6(x) + F_61(x))
Eq(F_54(x), F_17(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_17(x)*F_58(x))
Eq(F_58(x), F_26(x) + F_59(x))
Eq(F_59(x), F_57(x))
Eq(F_60(x), F_54(x))
Eq(F_61(x), F_17(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_49(x))
Eq(F_64(x), F_53(x))
Eq(F_65(x), F_66(x) + F_79(x))
Eq(F_66(x), F_6(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_17(x)*F_68(x))
Eq(F_68(x), F_33(x) + F_66(x))
Eq(F_69(x), F_17(x)*F_70(x))
Eq(F_70(x), F_25(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_17(x)*F_74(x))
Eq(F_74(x), F_26(x) + F_72(x))
Eq(F_75(x), 2*F_6(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_17(x)*F_77(x))
Eq(F_77(x), F_29(x) + F_75(x))
Eq(F_78(x), F_17(x)*F_71(x))
Eq(F_79(x), 2*F_6(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_17(x)*F_81(x))
Eq(F_81(x), F_36(x) + F_79(x))
Eq(F_82(x), F_17(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_66(x))
Eq(F_85(x), F_79(x))
Eq(F_86(x), F_17(x)*F_87(x))
Eq(F_87(x), F_5(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_11(x)*F_17(x)*F_28(x)*F_90(x))
Eq(F_90(x), F_28(x) + F_91(x))
Eq(F_91(x), F_26(x) + F_92(x))
Eq(F_92(x), F_6(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_17(x)*F_94(x))
Eq(F_94(x), F_26(x) + F_92(x))
Eq(F_95(x), F_17(x)*F_91(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"}, {"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": "point_and_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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"include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, 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{"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 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, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": 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