cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A005158 Number of alternating sign n X n matrices invariant under a half-turn.

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%I A005158 M0902 #53 Jan 08 2025 09:29:25
%S A005158 1,2,3,10,25,140,588,5544,39204,622908,7422987,198846076
%N A005158 Number of alternating sign n X n matrices invariant under a half-turn.
%D A005158 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A005158 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.
%H A005158 G. Kuperberg, <a href="https://arxiv.org/abs/math/0008184">Symmetry classes of alternating-sign matrices under one roof</a>, arXiv:math/0008184 [math.CO], 2000-2001.
%H A005158 D. P. Robbins, <a href="https://arxiv.org/abs/math/0008045">Symmetry classes of alternating sign matrices</a>, arXiv:math/0008045 [math.CO], 2000.
%H A005158 R. P. Stanley, <a href="/A005130/a005130.pdf">A baker's dozen of conjectures concerning plane partitions</a>, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]
%F A005158 Robbins gives simple (conjectured) formulas related to this sequence in Section 3.3.
%F A005158 a(n) = a(n-1) * (1 + [n even]/3) * C(n\2*3, n\2) / C(n\2*2, n\2) for all n > 1, where C(.,.) are the binomial coefficients, n\2 := floor(n/2) and [n even] = 1 if n is even, 0 else (Iverson bracket). [From Robbins conjectured(!) formulas.] - _M. F. Hasler_, Jun 15 2019
%Y A005158 A059475(n) = a(2n).
%K A005158 nonn,nice,more
%O A005158 1,2
%A A005158 _N. J. A. Sloane_