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.

6, 28, 340, 2304, 20652, 157926, 1313248, 10426852, 84878208, 681580848, 5513822118, 44425974796, 358734643924, 2893286239200, 23350243929660, 188381399097606, 1520085754764208, 12264581651146180, 98960550492317184, 798468925032585312

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: A049603 A333927 A035527 * A332465 A335290 A173360

Adjacent sequences: A220434 A220435 A220436 * A220438 A220439 A220440

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 16 2012

Status

approved