A287169 Number of non-attacking king positions on a cylindrical 3 X 2n chessboard.

1, 11, 67, 503, 3939, 31111, 246163, 1948503, 15424707, 122107175, 966645747, 7652334327, 60578794275, 479564842183, 3796418256467, 30053895424663, 237918103255427, 1883450483360871, 14910112659965107, 118034140795537975, 934403294669416419, 7397093003809879047

Offset: 0

Author

Richard M. Low, May 21 2017

Keywords

• nonn

Links

• Ray Chandler, 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 15.
• Index entries for linear recurrences with constant coefficients, signature (11, -27, 21, -4).

Crossrefs

Cf. A287120, A287168.

Programs

Mathematica

CoefficientList[Series[(1-27*x^2+42*x^3-12*x^4)/(1-11*x+27*x^2-21*x^3+4*x^4), {x, 0, 44}], x] (* Michael De Vlieger, May 21 2017; simplified by Georg Fischer, May 23 2019 *)

Formula

G.f.: (1-27*x^2+42*x^3-12*x^4)/(1-11*x+27*x^2-21*x^3+4*x^4). [Corrected by Georg Fischer, May 23 2019]