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A005162 Number of alternating sign n X n matrices symmetric with respect to both diagonals.
(Formerly M0877)
1
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

M. Bousquet-Mélou and L. Habsieger, Sur les matrices a signes alternants, Séries Formelles et Combinatoire Algébrique, 4th colloquium, 15-19 Juin 1992, Montréal, Université du Québec à Montréal, pp. 19-32.

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.

D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv:math.CO/0008045, 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 * A129108 A230284 A264235

Adjacent sequences:  A005159 A005160 A005161 * A005163 A005164 A005165

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane and Simon Plouffe

STATUS

approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)