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

0,2

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).

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]

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 *)

Crossrefs

Cf. A287120, A287168.

Sequence in context: A092841 A165673 A220511 * A120792 A228032 A145833

Adjacent sequences: A287166 A287167 A287168 * A287170 A287171 A287172

Keyword

nonn

Author

Richard M. Low, May 21 2017

Status

approved