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%I #20 Jan 09 2019 03:54:22
%S 6,28,340,2304,20652,157926,1313248,10426852,84878208,681580848,
%T 5513822118,44425974796,358734643924,2893286239200,23350243929660,
%U 188381399097606,1520085754764208,12264581651146180,98960550492317184,798468925032585312
%N 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.
%H Colin Barker, <a href="/A220437/b220437.txt">Table of n, a(n) for n = 0..1000</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1206.4864">Automatic Counting of Tilings of Skinny Plane Regions</a>, arXiv preprint arXiv:1206.4864 [math.CO], 2012.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (5,35,-67,-145,145,67,-35,-5,1).
%F 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)).
%t 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}]];
%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jan 09 2019 *)
%o (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
%Y Cf. A001654, A220438.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Dec 16 2012
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