0123_0213_0231_0321_3012
Counting sequence:
1, 1, 2, 6, 19, 56, 159, 441, 1204, 3251, 8709, 23196, 61519, 162641, 428964, 1129371, 2969389, 7799276, 20469399, 53690841, 140766964, 368937731, 966701589, 2532477756, 6633353119, 17372824481, 45495606084, 119134965291, 311951232829, 816802619276, 2138624397159, 5599406116521, 14660265041044, 38382731183891, 100490612865189, 263094476120796, 688803552915439, 1803337657462001, 4721252369143524, 12360505349314491, 32360435477491789, 84721144680544556, 221803685758909239, 580691286985717881, 1520272923977313844, 3980132982504362531, 10420137018652051509, 27280300063684347516, 71420807152866102079, 186982209355844180801, 489525996836526884484, 1281596132997457360971, 3355263105843286975069, 8784194591907287117516, 22997323484628341484039, 60207781491477271547721, 157626032248802541585364, 412670337772928490060851, 1080385026105979202302149, 2828484830617001664255516, 7405069645889010885284239, 19386724467338001181236881, 50755104476700933037705764, 132878590403916678690439131, 347880669617352864550729069, 910763424212749437995982956, 2384409614550110495505689559, 6242465442496012140658025241, 16342986759054786110742265204, 42786494926902066560116528451, 112016498206118854306702836309, 293263000060389377834183012796, 767772502712919042144228266719, 2010054509554107274495265916641, 5262391028900881833135097741764, 13777118583051496328497083825771, 36068964732059523359530266769789, 94429775636738906164441942552076, 247220362225380859962492013023399, 647231311133851003380427000792041, 1694473571365066809493574797900564, 4436189403339138743729869010005331, 11614094639407928058955175466306789, 30406094516395802707653943857297756, 79604188912801794613043229042351919, 208406472228054210229548889143288881, 545615227783450094271749730134576484, 1428439211146474588977992884754564091, 3739702405704330705446814091117362829, 9790668006063231592931619722574018476, 25632301612678792204486385744557680759, 67106236832360001282804218847005000121, 175686408885174924168479633468269272244, 459952989824712196271741406901426721891, 1204172560592056514744958037923258703989, 3152564691957647048159559608242845011196, 8253521515293264030126574589554267571839, 21607999853946903843005871765917940188801, 56570478046596965100462455919195517963524, 148103434285943026661524326413660543639691, 387739824811430185290396184165769972831389
Generating function in Maple syntax:
(x^5-x^4-x^3-4*x^2+4*x-1)/(2*x-1)/(x^2-3*x+1)
Generating function in latex syntax:
\frac{x^{5}-x^{4}-x^{3}-4 x^{2}+4 x -1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right)}
Generating function in sympy syntax:
(x**5 - x**4 - x**3 - 4*x**2 + 4*x - 1)/((2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2-3*x+1)*F(x)+x^5-x^4-x^3-4*x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}-3 x +1\right) F \! \left(x \right)+x^{5}-x^{4}-x^{3}-4 x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,5/4*(3/2-1/2*5^(1/2))^(1-n)+5/4*(3/2+1/2*5^(1/2))^(1-n)+1/8*(9*5^(1/2)-19)*(3/2-1/2*5^(1/2))^(-n)+1/8*(-9*5^(1/2)-19)*(3/2+1/2*5^(1/2))^(-n)-5/8*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{5 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{1-n}}{4}+\frac{5 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{1-n}}{4}+\frac{\left(9 \sqrt{5}-19\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{8}+\\\frac{\left(-9 \sqrt{5}-19\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{8}-\frac{5 \,2^{n}}{8} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(n+3) = 2*a(n)-7*a(n+1)+5*a(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) = 19
a \! \left(5\right) = 56
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16697/
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[16,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[53,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[10,x]+F[20,x]
F[20,x] = F[17,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[51,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[29,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[4,x]
F[29,x] = F[21,x]+F[30,x]
F[30,x] = 2*F[22,x]+F[31,x]+F[35,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[26,x]
F[34,x] = F[30,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[22,x]+F[38,x]+F[50,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = x^2
F[43,x] = F[37,x]+F[44,x]
F[44,x] = 2*F[22,x]+F[45,x]+F[49,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[41,x]
F[48,x] = F[44,x]
F[49,x] = F[37,x]*F[4,x]
F[50,x] = F[17,x]*F[4,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[17,x]+F[37,x]
F[53,x] = F[22,x]+F[54,x]+F[95,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[65,x]
F[56,x] = F[57,x]+F[7,x]
F[57,x] = F[22,x]+F[58,x]+F[60,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[11,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[4,x]
F[63,x] = F[64,x]
F[64,x] = x^2
F[65,x] = F[53,x]+F[66,x]
F[66,x] = F[22,x]+F[67,x]+F[71,x]+F[91,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[57,x]
F[70,x] = F[66,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[22,x]+F[51,x]+F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[81,x]
F[76,x] = F[11,x]+F[77,x]
F[77,x] = F[22,x]+F[58,x]+F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[4,x]+F[80,x]
F[80,x] = F[64,x]
F[81,x] = F[73,x]+F[82,x]
F[82,x] = F[22,x]+F[71,x]+F[83,x]+F[87,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[77,x]
F[86,x] = F[82,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[37,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[37,x]*F[4,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[37,x]
F[94,x] = F[90,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[17,x]+F[73,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[22,x]+F[38,x]
F[100,x] = F[4,x]*F[52,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_{16}\! \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_{14}\! \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_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{53}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \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_{51}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{26}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \left(x \right)+F_{50}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = x^{2}
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{53}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{95}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{65}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{22}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = x^{2}
F_{65}\! \left(x \right) = F_{53}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)+F_{91}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{57}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{81}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{22}\! \left(x \right)+F_{58}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{64}\! \left(x \right)
F_{81}\! \left(x \right) = F_{73}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{22}\! \left(x \right)+F_{71}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{77}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{37}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{37}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{17}\! \left(x \right)+F_{73}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{22}\! \left(x \right)+F_{38}\! \left(x \right)
F_{100}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \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_16(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_14(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_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_53(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_10(x) + F_20(x))
Eq(F_20(x), F_17(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_51(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_29(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_4(x))
Eq(F_29(x), F_21(x) + F_30(x))
Eq(F_30(x), 2*F_22(x) + F_31(x) + F_35(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_26(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_22(x) + F_38(x) + F_50(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), x**2)
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), 2*F_22(x) + F_45(x) + F_49(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_41(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_37(x)*F_4(x))
Eq(F_50(x), F_17(x)*F_4(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_17(x) + F_37(x))
Eq(F_53(x), F_22(x) + F_54(x) + F_95(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_65(x))
Eq(F_56(x), F_57(x) + F_7(x))
Eq(F_57(x), F_22(x) + F_58(x) + F_60(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_11(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_4(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), x**2)
Eq(F_65(x), F_53(x) + F_66(x))
Eq(F_66(x), F_22(x) + F_67(x) + F_71(x) + F_91(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_57(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_22(x) + F_51(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_81(x))
Eq(F_76(x), F_11(x) + F_77(x))
Eq(F_77(x), F_22(x) + F_58(x) + F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_4(x) + F_80(x))
Eq(F_80(x), F_64(x))
Eq(F_81(x), F_73(x) + F_82(x))
Eq(F_82(x), F_22(x) + F_71(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_77(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_37(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_37(x)*F_4(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_37(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_17(x) + F_73(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_22(x) + F_38(x))
Eq(F_100(x), F_4(x)*F_52(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 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], "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, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 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3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], 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0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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[0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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