A005158 - OEIS

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

(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

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