0123_1302_2031
Counting sequence:
1, 1, 2, 6, 21, 73, 243, 785, 2504, 7968, 25389, 81033, 258873, 827263, 2643616, 8447300, 26990489, 86236655, 275531223, 880341121, 2812760102, 8987010878, 28714292671, 91744697633, 293132350135, 936583428475, 2992465580300, 9561187907938, 30548827485851, 97606163247369, 311860190014571, 996420461723075, 3183650136538966, 10172039392531598, 32500551548324761, 103842092038304515, 331784525644315657, 1060080448088880231, 3387049333467167438, 10821917532887591934, 34576968788665235307, 110476425917955737939, 352981800058686022477, 1127807585530749914601, 3603443434672546539062, 11513315527819703676160, 36786045582864456088773, 117534618620921952385559, 375533340305564344169523, 1199861720195791144627821, 3833662668725424657799956, 12248886025950304793449578, 39136257370970662497575617, 125043749918313489276027035, 399525668625423762876683037, 1276519298204559079234302287, 4078590305086012272302479028, 13031451150122690663319022022, 41636621081129338667998278337, 133032629680480534734920654045, 425050835062234692151033811215, 1358074427462151617254927760805, 4339166044119415151078522474498, 13864013324824691724666807268160, 44296729721004173318650297263467, 141531908402180231000758754933395, 452206770615504504940010141661763, 1444840006038902698856599996569203, 4616389622404564571537238110566976, 14749766795473652275864314302778716, 47126789182828481796666413341810635, 150574194797731362573179525792133543, 481097662966742657051959069132413115, 1537148922648920867003043305965330463, 4911324648367863127482859462747204546, 15692109883600970214621995209378828488, 50137657399789031320037143620879803053, 160194180909072587707019622427442240581, 511834356210600644084143589335647365805, 1635355333825881320899200530195287965671, 5225102682971030855063906186645385529586, 16694658025005051763566543020449971595760, 53340886004059954167412604777490816236707, 170428775206807995634733358811404304185873, 544534776124301825837848234814688266669893, 1739836022695882835551780486293828716941133, 5558927581108692468928833171443769100616594, 17761257640894610904688635274107345846903586, 56748764646313358007062677306456520314433409, 181317244194902432654353706540131678237016233, 579324382606972599711108407945125451924797503, 1850991844560505031045731508976654493901931557, 5914080110372113146784623088044191796624172248, 18896000895240963823419289537545883876161666036, 60374368146744838421680859363119844835689495313, 192901363062313483526640084833728872378951148153, 616336651024723911760596740145572875782089318333, 1969249264836254813423379631410530690557948101611, 6291922864899639243884520680707832683257058654032, 20103241394958038979244696318350320913701272605280, 64231606658515635438724262821239921579740103796421
Generating function in Maple syntax:
-(x^3-2*x^2+3*x-1)*(x-1)^3/(x^7-4*x^6+12*x^5-23*x^4+28*x^3-19*x^2+7*x-1)
Generating function in latex syntax:
-\frac{\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}{x^{7}-4 x^{6}+12 x^{5}-23 x^{4}+28 x^{3}-19 x^{2}+7 x -1}
Generating function in sympy syntax:
(x - 1)**3*(-x**3 + 2*x**2 - 3*x + 1)/(x**7 - 4*x**6 + 12*x**5 - 23*x**4 + 28*x**3 - 19*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^7-4*x^6+12*x^5-23*x^4+28*x^3-19*x^2+7*x-1)*F(x)+(x^3-2*x^2+3*x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}-4 x^{6}+12 x^{5}-23 x^{4}+28 x^{3}-19 x^{2}+7 x -1\right) F \! \left(x \right)+\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+5)-12189/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+5)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+4)+56185/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+4)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+3)-304023/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+3)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+2)+607623/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+2)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+1)-684809/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n-1)-37819/623962*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n-1)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n)+213366/311981*RootOf(_Z^7-4*_Z^6+12*_Z^5-23*_Z^4+28*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n)
Explicit closed form in latex syntax:
-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{311981}-\frac{12189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{311981}+\frac{56185 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{311981}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{623962}-\frac{304023 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{623962}+\frac{607623 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{623962}-\frac{684809 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{623962}-\frac{37819 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{623962}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{311981}+\frac{213366 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-4 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}-23 \textit{\_Z}^{4}+28 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{311981}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 243
a(n+7) = a(n)-4*a(n+1)+12*a(n+2)-23*a(n+3)+28*a(n+4)-19*a(n+5)+7*a(n+6), n >= 7
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) = 243
a \! \left(n +7\right) = a \! \left(n \right)-4 a \! \left(n +1\right)+12 a \! \left(n +2\right)-23 a \! \left(n +3\right)+28 a \! \left(n +4\right)-19 a \! \left(n +5\right)+7 a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14673/
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[23,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[11,x]
F[19,x] = F[14,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[7,x]
F[22,x] = F[20,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = F[15,x]+F[25,x]+F[60,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[33,x]
F[27,x] = F[28,x]+F[7,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[18,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[29,x]
F[33,x] = F[24,x]+F[34,x]
F[34,x] = 2*F[15,x]+F[35,x]+F[39,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[28,x]
F[38,x] = F[34,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[55,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]+F[43,x]+F[52,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[11,x]+F[32,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = 2*F[15,x]+F[39,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[32,x]
F[51,x] = F[47,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[2,x]+F[54,x]
F[54,x] = F[52,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[42,x]
F[59,x] = F[56,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[2,x]+F[42,x]
F[63,x] = F[64,x]+F[76,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[53,x]+F[67,x]
F[67,x] = F[64,x]+F[68,x]
F[68,x] = 2*F[15,x]+F[69,x]+F[73,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[54,x]
F[72,x] = F[68,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[64,x]+F[75,x]
F[75,x] = F[73,x]
F[76,x] = 2*F[15,x]+F[73,x]+F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[58,x]+F[79,x]
F[79,x] = F[76,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_{23}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{22}\! \left(x \right) = F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{60}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \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_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{28}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{55}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{52}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \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_{42}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \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_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{76}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{53}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{64}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{58}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{76}\! \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_23(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_11(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_7(x))
Eq(F_22(x), F_20(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_60(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_33(x))
Eq(F_27(x), F_28(x) + F_7(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_18(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_29(x))
Eq(F_33(x), F_24(x) + F_34(x))
Eq(F_34(x), 2*F_15(x) + F_35(x) + F_39(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_28(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_55(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x) + F_43(x) + F_52(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_11(x) + F_32(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), 2*F_15(x) + F_39(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_32(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_2(x) + F_54(x))
Eq(F_54(x), F_52(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_42(x))
Eq(F_59(x), F_56(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_2(x) + F_42(x))
Eq(F_63(x), F_64(x) + F_76(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_53(x) + F_67(x))
Eq(F_67(x), F_64(x) + F_68(x))
Eq(F_68(x), 2*F_15(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_54(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_64(x) + F_75(x))
Eq(F_75(x), F_73(x))
Eq(F_76(x), 2*F_15(x) + F_73(x) + F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_58(x) + F_79(x))
Eq(F_79(x), F_76(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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