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

0,2

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).

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).

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 *)

Prog

(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

Crossrefs

Cf. A287168, A287169.

Sequence in context: A244834 A169831 A212095 * A127813 A295911 A231791

Adjacent sequences: A287117 A287118 A287119 * A287121 A287122 A287123

Keyword

nonn,easy

Author

Richard M. Low, May 20 2017

Status

approved