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A340535
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Number of domino tilings (or dimer coverings) of the 2n X n grid.
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1
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1, 1, 5, 41, 2245, 185921, 106912793, 90124167441, 540061286536921, 4652799879944138561, 289415868852204573601981, 25545661075321867247577262777, 16457725663617130715785831809325501, 14905470663149838513993965664256435411841, 99323759360556656337166635121447749135517599089
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 5:
.___. .___. .___. .___. .___.
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|___| | | | |_|_| |___| | | |
|___| |_|_| |___| |___| |_|_|
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MAPLE
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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);
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MATHEMATICA
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T[_?OddQ, _?OddQ] = 0;
T[m_, n_] := Product[2(2+Cos[2 j Pi/(m+1)]+Cos[2 k Pi/(n+1)]), {k, 1, n/2}, {j, 1, m/2}];
a[n_] := T[2n, n] // Round;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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