This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195657 #13 Aug 28 2024 13:20:19 %S A195657 512,17536,218052,1599820,8500668,36383284,133538996,437500380, %T A195657 1314748124,3694894500,9849731140,25173962492,62193359676, %U A195657 149475988116,351246183572,810197361564,1840289301660,4126688132548,9154339355684,20122502355004,43888598831484 %N A195657 Number of ways to place 8n nonattacking kings on a vertical cylinder 16 X 2n. %C A195657 Vertical cylinder: a chessboard where it is supposed that the columns 1 and 16 are in contact (number of columns = 16, number of rows = 2n). %H A195657 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a> %H A195657 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (11, -53, 147, -259, 301, -231, 113, -32, 4). %F A195657 Recurrence: a(n) = 4*a(n-9) - 32*a(n-8) + 113*a(n-7) - 231*a(n-6) + 301*a(n-5) - 259*a(n-4) + 147*a(n-3) - 53*a(n-2) + 11*a(n-1). %F A195657 G.f.: -(1 + 501*x + 11957*x^2 + 52145*x^3 + 55651*x^4 + 13919*x^5 + 695*x^6 + 27*x^7)/((x-1)^7*(2*x-1)^2). %F A195657 a(n) = (1751437*n - 15876635)*2^n + 8431/45*n^6 + 22263/5*n^5 + 500633/9*n^4 + 1381699/3*n^3 + 117001024/45*n^2 + 138801256/15*n + 15876636. %Y A195657 Cf. A195652, A174558, A137432. %K A195657 nonn %O A195657 1,1 %A A195657 _Vaclav Kotesovec_, Sep 22 2011