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 A005158 Number of alternating sign n X n matrices invariant under a half-turn. (Formerly M0902) 4
 1, 2, 3, 10, 25, 140, 588, 5544, 39204, 622908, 7422987, 198846076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. LINKS D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv:math.CO/0008045 R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy] FORMULA Robbins gives a simple (conjectured) formula. MATHEMATICA a[n_?OddQ] := a[n] = (a[n-1]*Binomial[(3*(n-1))/2, (n-1)/2])/ Binomial[n-1, (n-1)/2]; a[n_?EvenQ] := a[n] = (4*a[n-1]*Binomial[(3*n)/2, n/2])/ (3*Binomial[n, n/2]); a[1] = 1; Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Sep 12 2012, from Robbins's conjectured(!) formula *) PROG (PARI) /* from Robbins's conjectured(!) formula */ /* using memoization for efficiency */ N=33;  v=vector(N); v[1]=1; { for (n=2, N,     if (bitand(n, 1),         v[n] = (v[n-1]*binomial((3*(n-1))/2, (n-1)/2)) / binomial(n-1, (n-1)/2);     ,         v[n] = (4*v[n-1]*binomial((3*n)/2, n/2))/ (3*binomial(n, n/2));     ); ); } v /* show terms */ /* Joerg Arndt, Sep 12 2012 */ CROSSREFS a(2n) gives A059475. Sequence in context: A123029 A103018 A246437 * A182926 A005225 A211208 Adjacent sequences:  A005155 A005156 A005157 * A005159 A005160 A005161 KEYWORD nonn,nice,more AUTHOR STATUS approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)