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A340535 Number of domino tilings (or dimer coverings) of the 2n X n grid. 1
1, 1, 5, 41, 2245, 185921, 106912793, 90124167441, 540061286536921, 4652799879944138561, 289415868852204573601981, 25545661075321867247577262777, 16457725663617130715785831809325501, 14905470663149838513993965664256435411841, 99323759360556656337166635121447749135517599089 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..63

FORMULA

a(n) = A187596(2n,n) = A187596(n,2n) = A187616(2n,n).

a(n) = A099390(2n,n) = A099390(n,2n) for n >= 1.

EXAMPLE

a(2) = 5:

   .___.   .___.   .___.   .___.   .___.

   |___|   |___|   |___|   | | |   | | |

   |___|   |___|   | | |   |_|_|   |_|_|

   |___|   | | |   |_|_|   |___|   | | |

   |___|   |_|_|   |___|   |___|   |_|_|

.

MAPLE

b:= proc(m, n) option remember; local i, j, t, M;

       M:= Matrix(n*m, shape=skewsymmetric);

       for i to n do for j to m do t:= (i-1)*m+j;

          if j<m then M[t, t+1]:= 1 fi;

          if i<n then M[t, t+m]:= 1-2*irem(j, 2) fi

       od od;

       isqrt(LinearAlgebra[Determinant](M))

    end:

a:= n-> b(2*n, n):

seq(a(n), n=0..15);

CROSSREFS

Cf. A004003, A099390, A187596, A187616.

Sequence in context: A318294 A093433 A065035 * A145008 A216610 A025173

Adjacent sequences:  A340532 A340533 A340534 * A340536 A340537 A340538

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 10 2021

STATUS

approved

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Last modified August 5 21:02 EDT 2021. Contains 346488 sequences. (Running on oeis4.)