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%I #17 Jul 07 2020 04:20:27
%S 1,1,144,780,51205,380160,21001799,170537640,8940739824,74795194705,
%T 3852472573499,32565539635200,1666961188795475,14143261515284447,
%U 722364079570222320,6136973985625588560,313196612952258199679,2662079368040434932480,135818983640055277506397
%N Number of domino tilings of the 11 X n grid with upper left corner removed iff n is odd.
%H Alois P. Heinz, <a href="/A210724/b210724.txt">Table of n, a(n) for n = 0..250</a>
%H <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%F a(n) = 780*a(n-2) -194881*a(n-4) +22377420*a(n-6)
%F -1419219792*a(n-8) +55284715980*a(n-10)
%F -1410775106597*a(n-12) +24574215822780*a(n-14)
%F -300429297446885*a(n-16) +2629946465331120*a(n-18)
%F -16741727755133760*a(n-20) +78475174345180080*a(n-22)
%F -273689714665707178*a(n-24) +716370537293731320*a(n-26)
%F -1417056251105102122*a(n-28) +2129255507292156360*a(n-30)
%F -2437932520099475424*a(n-32) +2129255507292156360*a(n-34)
%F -1417056251105102122*a(n-36) +716370537293731320*a(n-38)
%F -273689714665707178*a(n-40) +78475174345180080*a(n-42)
%F -16741727755133760*a(n-44) +2629946465331120*a(n-46)
%F -300429297446885*a(n-48) +24574215822780*a(n-50)
%F -1410775106597*a(n-52) +55284715980*a(n-54)
%F -1419219792*a(n-56) +22377420*a(n-58)
%F -194881*a(n-60) +780*a(n-62) -a(n-64).
%t A[1, 1] = 1;
%t 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}]] ]]];
%t a[n_] := A[11, n];
%t a /@ Range[0, 18] (* _Jean-François Alcover_, Feb 27 2020, after _Alois P. Heinz_ in A189006 *)
%Y 11th row of array A189006.
%Y Bisection gives: A028473 (even part), A139400 (odd part).
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Mar 30 2012
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