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A194644 Number of ways to place 2n nonattacking kings on a 4 X 2n cylindrical chessboard. 9
12, 32, 90, 256, 732, 2102, 6060, 17536, 50922, 148352, 433500, 1270246, 3731532, 10987232, 32418810, 95835136, 283784412, 841611542, 2499330540, 7431221056, 22118855562, 65898914432, 196498594140, 586358987206, 1750864725132, 5231094261152, 15636995277210 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 4, number of rows = 2n).

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..2091

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights

Index entries for linear recurrences with constant coefficients, signature (6,-10,3).

FORMULA

a(n) = 2*3^n + 2*((3+sqrt(5))/2)^n + 2*((3-sqrt(5))/2)^n.

Recurrence: a(n) = 3*a(n-3) - 10*a(n-2) + 6*a(n-1).

G.f.: -2*(3-12*x+10*x^2)/((-1+3*x)*(1-3*x+x^2)).

MATHEMATICA

Table[2*3^n+2*LucasL[2n], {n, 25}]

Drop[CoefficientList[Series[-2*(3 - 12*x + 10*x^2)/((-1 + 3*x)*(1 - 3*x + x^2)), {x, 0, 27}], x], 1] (* or *) LinearRecurrence[{6, -10, 3}, {12, 32, 90}, 27] (* Indranil Ghosh, Mar 05 2017 *)

PROG

(PARI) print(Vec(-2*(3 - 12*x + 10*x^2)/((-1 + 3*x)*(1 - 3*x + x^2)) + O(x^27))); \\ Indranil Ghosh, Mar 05 2017

CROSSREFS

Cf. A061593, A137432, A195590.

Sequence in context: A183682 A243027 A242543 * A068381 A143238 A102091

Adjacent sequences:  A194641 A194642 A194643 * A194645 A194646 A194647

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Aug 31 2011

STATUS

approved

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Last modified January 25 04:21 EST 2022. Contains 350565 sequences. (Running on oeis4.)