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A210724
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Number of domino tilings of the 11 X n grid with upper left corner removed iff n is odd.
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4
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1, 1, 144, 780, 51205, 380160, 21001799, 170537640, 8940739824, 74795194705, 3852472573499, 32565539635200, 1666961188795475, 14143261515284447, 722364079570222320, 6136973985625588560, 313196612952258199679, 2662079368040434932480, 135818983640055277506397
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 780*a(n-2) -194881*a(n-4) +22377420*a(n-6)
-1419219792*a(n-8) +55284715980*a(n-10)
-1410775106597*a(n-12) +24574215822780*a(n-14)
-300429297446885*a(n-16) +2629946465331120*a(n-18)
-16741727755133760*a(n-20) +78475174345180080*a(n-22)
-273689714665707178*a(n-24) +716370537293731320*a(n-26)
-1417056251105102122*a(n-28) +2129255507292156360*a(n-30)
-2437932520099475424*a(n-32) +2129255507292156360*a(n-34)
-1417056251105102122*a(n-36) +716370537293731320*a(n-38)
-273689714665707178*a(n-40) +78475174345180080*a(n-42)
-16741727755133760*a(n-44) +2629946465331120*a(n-46)
-300429297446885*a(n-48) +24574215822780*a(n-50)
-1410775106597*a(n-52) +55284715980*a(n-54)
-1419219792*a(n-56) +22377420*a(n-58)
-194881*a(n-60) +780*a(n-62) -a(n-64).
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MATHEMATICA
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A[1, 1] = 1;
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[11, 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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