A005158 Number of alternating sign n X n matrices invariant under a half-turn. (Formerly M0902)

1, 2, 3, 10, 25, 140, 588, 5544, 39204, 622908, 7422987, 198846076

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

Table of n, a(n) for n=1..12.

G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001.

D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv:math/0008045 [math.CO], 2000.

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 simple (conjectured) formulas related to this sequence in Section 3.3.

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

Crossrefs

A059475(n) = a(2n).

Sequence in context: A103018 A246437 A341265 * A370608 A182926 A005225

Adjacent sequences: A005155 A005156 A005157 * A005159 A005160 A005161

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Status

approved