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A189004 Number of domino tilings of the 7 X n grid with upper left corner removed iff n is odd. 3
1, 1, 21, 56, 781, 2415, 31529, 100352, 1292697, 4140081, 53175517, 170537640, 2188978117, 7022359583, 90124167441, 289143013376, 3710708201969, 11905151192865, 152783289861989, 490179860527896, 6290652543875133 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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).
FORMULA
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).
MATHEMATICA
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];
a /@ Range[0, 20] (* Jean-François Alcover, Feb 27 2020, after Alois P. Heinz in A189006 *)
CROSSREFS
7th row of array A189006.
Bisection gives: A028469 (even part), A003696 (odd part).
Sequence in context: A254144 A165237 A271734 * A183310 A280884 A257103
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Apr 15 2011
STATUS
approved

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Last modified May 25 01:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)