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A220437 Number of domino tilings of a cross whose center is a 4 X 4 square and in which each of the four arms has length n. 2
6, 28, 340, 2304, 20652, 157926, 1313248, 10426852, 84878208, 681580848, 5513822118, 44425974796, 358734643924, 2893286239200, 23350243929660, 188381399097606, 1520085754764208, 12264581651146180, 98960550492317184, 798468925032585312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Shalosh B. Ekhad and Doron Zeilberger, Automatic Counting of Tilings of Skinny Plane Regions, arXiv preprint arXiv:1206.4864 [math.CO], 2012.

Index entries for linear recurrences with constant coefficients, signature (5,35,-67,-145,145,67,-35,-5,1).

FORMULA

G.f.: -2*(3 -x- 5*x^2 + 13*x^3 - 11*x^4 - 2*x^5 + 2*x^6)/((x - 1)*(x^4 - 11*x^3 + 25*x^2 - 11*x+ 1)*(x^4 + 7*x^3 + 13*x^2 + 7*x+ 1)).

MATHEMATICA

a = DifferenceRoot[Function[{a, n}, {a[n] - 4 a[n+1] - 39 a[n+2] + 28 a[n+3] + 173 a[n+4] + 28 a[n+5] - 39 a[n+6] - 4 a[n+7] + a[n+8] + 2 == 0, a[0] == 6, a[1] == 28, a[2] == 340, a[3] == 2304, a[4] == 20652, a[5] == 157926, a[6] == 1313248, a[7] == 10426852}]];

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 09 2019 *)

PROG

(PARI) Vec(-2*(2*x^6-2*x^5-11*x^4+13*x^3-5*x^2-x+3) / ((x-1)*(x^4-11*x^3+25*x^2-11*x+1)*(x^4+7*x^3+13*x^2+7*x+1)) + O(x^100)) \\ Colin Barker, May 25 2015

CROSSREFS

Cf. A001654, A220438.

Sequence in context: A281003 A049603 A035527 * A173360 A085844 A325638

Adjacent sequences:  A220434 A220435 A220436 * A220438 A220439 A220440

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 16 2012

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)