

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, 29540545024, 1259111024288, 64726478396896, 4641989615977216, 404396533544588344, 48825344233129714772
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OFFSET

0,4


REFERENCES

M. BousquetMélou and L. Habsieger, Sur les matrices à signes alternants, Séries Formelles et Combinatoire Algébrique, 4th colloquium, 1519 Juin 1992, Montréal, Université du Québec à Montréal, pp. 1932.
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. 285293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.


LINKS

Table of n, a(n) for n=0..19.
C. Hagendorf and J. Liénardy The open XXZ chain at ∆ = 1/2 and the boundary quantum KnizhnikZamolodchikov equations, arXiv:2008.03220 [mathph], 2020.
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. 285293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]


FORMULA

Hagendorf and Liénardy give a (conjectured) formula in terms of multiple contour integrals.  Jean Liénardy, Aug 15 2020


CROSSREFS

Cf. A005130.
Sequence in context: A153930 A284107 A184177 * A246494 A334444 A268951
Adjacent sequences: A005161 A005162 A005163 * A005165 A005166 A005167


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane and Simon Plouffe


EXTENSIONS

a(14)a(19) from Jean Liénardy, Aug 15 2020


STATUS

approved



