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 A230879 Number of 2-packed n X n matrices. 3
 1, 2, 56, 16064, 39156608, 813732073472, 147662286695991296, 237776857718965784182784, 3425329990022686416530808209408, 443021337239562368918979788606843912192, 515203019085226443540506018909263027730003787776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..30 H. Cheballah, S. Giraudo, R. Maurice, Combinatorial Hopf algebra structure on packed square matrices, arXiv preprint arXiv:1306.6605 [math.CO], 2013. FORMULA 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 MATHEMATICA 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]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Oct 08 2017, translated from PARI *) PROG (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)))} a(n) = p(2, n); \\ Andrew Howroyd, Sep 20 2017 CROSSREFS Row sums of A230878. Cf. A048291, A055599, A230880, A104602. Sequence in context: A325291 A326551 A253471 * A080318 A002542 A264939 Adjacent sequences: A230876 A230877 A230878 * A230880 A230881 A230882 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 09 2013 EXTENSIONS Terms a(7) and beyond from Andrew Howroyd, Sep 20 2017 STATUS approved

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Last modified August 10 00:01 EDT 2024. Contains 375044 sequences. (Running on oeis4.)