A189005 Number of domino tilings of the 9 X n grid with upper left corner removed iff n is odd.

1, 1, 55, 209, 6336, 30305, 817991, 4140081, 108435745, 557568000, 14479521761, 74795194705, 1937528668711, 10021992194369, 259423766712000, 1342421467113969, 34741645659770711, 179796299139278305, 4652799879944138561

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Index entries for sequences related to dominoes

Formula

G.f.: -(x^30+x^29-154*x^28 +6777*x^26-1440*x^25-123961*x^24 +26752*x^23 +1132714*x^22-185889*x^21 -5684515*x^20+574750*x^19+16401668*x^18 -708928*x^17 -27757938*x^16+27757938*x^14+708928*x^13 -16401668*x^12 -574750*x^11+5684515*x^10 +185889*x^9-1132714*x^8-26752*x^7 +123961*x^6 +1440*x^5-6777*x^4+154*x^2-x-1) / (x^32-209*x^30+11936*x^28 -274208*x^26 +3112032*x^24-19456019*x^22 +70651107*x^20-152325888*x^18+196664896*x^16 -152325888*x^14+70651107*x^12 -19456019*x^10 +3112032*x^8-274208*x^6 +11936*x^4-209*x^2+1).

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

Crossrefs

9th row of array A189006.

Bisection gives: A028471 (even part), A003779 (odd part).

Sequence in context: A178793 A334531 A161763 * A105442 A158646 A294461

Adjacent sequences: A189002 A189003 A189004 * A189006 A189007 A189008

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 15 2011

Status

approved