A288637 Number of cycles in the grid graph P_4 X P_{n+1}.

6, 40, 213, 1049, 5034, 23984, 114069, 542295, 2577870, 12253948, 58249011, 276885683, 1316170990, 6256394122, 29739651711, 141366874247, 671984773580, 3194266961582, 15183887824311, 72176324719925, 343088799809408, 1630866146364842, 7752291502484181

Offset: 1

Author

Andrew Howroyd, Jun 12 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Row 3 of A231829.

Formula

Empirical: a(n) = 9*a(n-1)-27*a(n-2)+38*a(n-3)-29*a(n-4)+11*a(n-5)+a(n-6)-2*a(n-7) for n>7.

Empirical g.f.: x*(6 - 14*x + 15*x^2 - 16*x^3 - 2*x^4 + x^5) / ((1 - x)^2*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)). - Colin Barker, Jun 12 2017