A287120 Number of non-attacking bishop positions on a 3 X n chessboard.

1, 8, 25, 70, 225, 748, 2401, 7668, 24649, 79344, 255025, 819494, 2634129, 8467464, 27217089, 87483296, 281199361, 903867144, 2905317801, 9338615022, 30017295025, 96485195716, 310134268609, 996870677460, 3204261102025, 10299519778080, 33105949765729, 106413107836334

Offset: 0

Author

Richard M. Low, May 20 2017

Keywords

• nonn
• easy

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 1.
• Index entries for linear recurrences with constant coefficients, signature (3,0,2,4,-10,-2,0,-1,1).

Crossrefs

Cf. A287168, A287169.

Programs

Mathematica

CoefficientList[Series[(-1 - 5 x - x^2 + 7 x^3 + 5 x^4 - x^5 + x^6 - x^7)/(-1 + 3 x + 2 x^3 + 4 x^4 - 10 x^5 - 2 x^6 - x^8 + x^9), {x, 0, 27}], x] (* Michael De Vlieger, May 20 2017 *)

PARI

Vec((-1-5*x-x^2+7*x^3+5*x^4-x^5+x^6-x^7)/ (-1+3*x+2*x^3 +4*x^4-10*x^5-2*x^6-x^8+x^9) + O(x^30)) \\ Michel Marcus, May 20 2017

Formula

G.f.: (-1-5*x-x^2+7*x^3+5*x^4-x^5+x^6-x^7) / (-1+3*x +2*x^3 +4*x^4 -10*x^5 -2*x^6 -x^8 +x^9).