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A189004
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Number of domino tilings of the 7 X n grid with upper left corner removed iff n is odd.
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3
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1, 1, 21, 56, 781, 2415, 31529, 100352, 1292697, 4140081, 53175517, 170537640, 2188978117, 7022359583, 90124167441, 289143013376, 3710708201969, 11905151192865, 152783289861989, 490179860527896, 6290652543875133
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 56, 0, -672, 0, 2632, 0, -4094, 0, 2632, 0, -672, 0, 56, 0, -1).
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FORMULA
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G.f.: -(x^14-x^13-35*x^12+277*x^10 +49*x^9-727*x^8 -112*x^7+727*x^6 +49*x^5-277*x^4 +35*x^2-x-1) / (x^16-56*x^14 +672*x^12-2632*x^10 +4094*x^8-2632*x^6 +672*x^4-56*x^2+1).
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MATHEMATICA
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A[m_, n_] := A[m, n] = Module[{i, j, s, t, M}, Which[m == 0 || n == 0, 1, m < n, A[n, m], True, s = Mod[n*m, 2]; M[i_, j_] /; j < i := -M[j, i]; M[_, _] = 0; For[i = 1, i <= n, i++, For[j = 1, j <= m, j++, t = (i - 1)*m + j - s; If[i > 1 || j > 1 || s == 0, If[j < m, M[t, t + 1] = 1]; If[i < n, M[t, t + m] = 1 - 2*Mod[j, 2]]]]]; Sqrt[Det[Array[M, {n*m - s, n*m - s}]] ]]];
a[n_] := A[7, n];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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