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A210724 Number of domino tilings of the 11 X n grid with upper left corner removed iff n is odd. 4
1, 1, 144, 780, 51205, 380160, 21001799, 170537640, 8940739824, 74795194705, 3852472573499, 32565539635200, 1666961188795475, 14143261515284447, 722364079570222320, 6136973985625588560, 313196612952258199679, 2662079368040434932480, 135818983640055277506397 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Index entries for sequences related to dominoes

FORMULA

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).

MATHEMATICA

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];

a /@ Range[0, 18] (* Jean-François Alcover, Feb 27 2020, after Alois P. Heinz in A189006 *)

CROSSREFS

11th row of array A189006.

Bisection gives: A028473 (even part), A139400 (odd part).

Sequence in context: A233646 A268806 A112067 * A237738 A237734 A234091

Adjacent sequences: A210721 A210722 A210723 * A210725 A210726 A210727

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Mar 30 2012

STATUS

approved

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Last modified November 27 22:56 EST 2022. Contains 358406 sequences. (Running on oeis4.)