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

0,2

Comments

Essentially the same as A081069. - R. J. Mathar, May 25 2017

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).

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

Prog

(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

Crossrefs

Sequence in context: A199411 A069665 A188235 * A066558 A168597 A169724

Adjacent sequences: A286807 A286808 A286809 * A286811 A286812 A286813

Keyword

nonn,easy

Author

Richard M. Low, May 20 2017

Status

approved