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A230879
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Number of 2-packed n X n matrices.
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3
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1, 2, 56, 16064, 39156608, 813732073472, 147662286695991296, 237776857718965784182784, 3425329990022686416530808209408, 443021337239562368918979788606843912192, 515203019085226443540506018909263027730003787776
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OFFSET
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0,2
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COMMENTS
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A k-packed matrix of size n X n is a matrix with entries in the alphabet A_k = {0,1, ..., k} such that each row and each column contains at least one nonzero entry.
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LINKS
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FORMULA
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Cheballah et al. give an explicit formula.
a(n) = Sum_{i=0..n} Sum_{j=0..n} (-1)^(i+j) * binomial(n,i) * binomial(n,j) * 3^(i*j). - Andrew Howroyd, Sep 20 2017
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MATHEMATICA
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p[k_, n_] := Sum[(-1)^(i + j)*Binomial[n, i]*Binomial[n, j]*(k + 1)^(i*j), {i, 0, n}, {j, 0, n}];
a[n_] := p[2, n];
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PROG
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(PARI) \\ here p(k, n) is number of k-packed matrices of size n.
p(k, n)={sum(i=0, n, sum(j=0, n, (-1)^(i+j) * binomial(n, i) * binomial(n, j) * (k+1)^(i*j)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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