A005162 Number of alternating sign n X n matrices symmetric with respect to both diagonals. (Formerly M0877)

1, 2, 3, 8, 15, 52, 126, 568, 1782, 10436, 42471, 323144, 1706562, 16866856, 115640460, 1484714416, 13216815036, 220426128584, 2548124192970

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..19.

Mireille Bousquet-Mélou and Laurent Habsieger, Sur les matrices à signes alternants, [On alternating-sign matrices] in Formal power series and algebraic combinatorics (Montreal, PQ, 1992) pp. 19-32; Discrete Math. 139 (1995), 57-72. See Table 1, p. 71.

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 a simple (conjectured) formula.

Crossrefs

Sequence in context: A080498 A148013 A133983 * A350654 A129108 A230284

Adjacent sequences: A005159 A005160 A005161 * A005163 A005164 A005165

Keyword

nonn,nice,more

Author

N. J. A. Sloane and Simon Plouffe

Status

approved