A005162 - OEIS

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

(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..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