A005164 Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square.
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
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
- 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]
Crossrefs
Cf. A005130.
Formula
Hagendorf and Liénardy give a (conjectured) formula in terms of multiple contour integrals. - Jean Liénardy, Aug 15 2020
Extensions
a(14)-a(19) from Jean Liénardy, Aug 15 2020
a(20)-a(24) from Jean Liénardy, Sep 21 2022