A286810 Number of non-attacking bishop positions on a cylindrical 2 X 2n chessboard.
1, 9, 49, 324, 2209, 15129, 103684, 710649, 4870849, 33385284, 228826129, 1568397609, 10749957124, 73681302249, 505019158609, 3461452808004, 23725150497409, 162614600673849, 1114577054219524, 7639424778862809, 52361396397820129, 358890350005878084, 2459871053643326449, 16860207025497407049
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Richard M. Low and Ardak Kapbasov, Non-Attacking Bishop and King Positions on Regular and Cylindrical Chessboards, Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.1, Table 9.
- Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
Programs
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PARI
Vec((1 + x - 15*x^2 + 3*x^3) / ((1 - x)*(1 - 7*x + x^2)) + O(x^30)) \\ Colin Barker, May 21 2017
Formula
G.f.: (1+x^2-15*x^4+3*x^6) / (1-8*x^2+8*x^4-x^6).
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3) for n>3. - Colin Barker, May 21 2017
Comments