A005164 Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square. (Formerly M1271)

1, 1, 1, 2, 4, 13, 46, 248, 1516, 13654, 142873, 2156888, 38456356, 974936056, 29540545024, 1259111024288, 64726478396896, 4641989615977216, 404396533544588344, 48825344233129714772, 7202552030561982627472, 1464587581921220811285325, 365627222082497915618219716, 125253905685915522767942493032, 52893528399758443649956432899616

Offset

0,4

References

M. Bousquet-Mélou and L. Habsieger, Sur les matrices à 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..24.

C. Hagendorf and J. Liénardy The open XXZ chain at ∆ = -1/2 and the boundary quantum Knizhnik-Zamolodchikov equations, arXiv:2008.03220 [math-ph], 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. 285-293 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 A362642 A334444

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

a(20)-a(24) from Jean Liénardy, Sep 21 2022

Status

approved