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A005164 Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square.
(Formerly M1271)
3
1, 1, 1, 2, 4, 13, 46, 248, 1516, 13654, 142873, 2156888, 38456356, 974936056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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=0..13.

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

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

Cf. A005130, A057628.

Sequence in context: A153930 A284107 A184177 * A246494 A268951 A290722

Adjacent sequences:  A005161 A005162 A005163 * A005165 A005166 A005167

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane and Simon Plouffe

STATUS

approved

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Last modified June 20 03:20 EDT 2018. Contains 305608 sequences. (Running on oeis4.)