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A195592 Number of ways to place 4n nonattacking kings on a vertical cylinder 8 X 2n. 1
32, 256, 1220, 4460, 13932, 39316, 103508, 259372, 626780, 1473764, 3392964, 7682812, 17166476, 37942900, 83115188, 180699980, 390351420, 838619524, 1793087780, 3817890076, 8099228012, 17125372436, 36104600340, 75916936300, 159249370652, 333329766436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 8 are in contact (number of columns = 8, number of rows = 2n).

LINKS

Table of n, a(n) for n=1..26.

V. Kotesovec, Non-attacking chess pieces

Index entries for linear recurrences with constant coefficients, signature (7, -19, 25, -16, 4).

FORMULA

Recurrence: a(n) = 4*a(n-5) - 16*a(n-4) + 25*a(n-3) - 19*a(n-2) + 7*a(n-1).

G.f.: -(1 + 25*x + 51*x^2 + 11*x^3)/((x-1)^3*(2*x-1)^2).

a(n) = (221*n - 779)*2^n + 44*n^2 + 324*n + 780.

MATHEMATICA

LinearRecurrence[{7, -19, 25, -16, 4}, {32, 256, 1220, 4460, 13932}, 30] (* Harvey P. Dale, Jan 15 2016 *)

CROSSREFS

Cf. A194646, A173782, A137432.

Sequence in context: A231801 A250280 A159982 * A097243 A022327 A318022

Adjacent sequences:  A195589 A195590 A195591 * A195593 A195594 A195595

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 21 2011

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)