cp's OEIS Frontend

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

%I A005164 M1271 #41 Sep 21 2022 08:53:45
%S A005164 1,1,1,2,4,13,46,248,1516,13654,142873,2156888,38456356,974936056,
%T A005164 29540545024,1259111024288,64726478396896,4641989615977216,
%U A005164 404396533544588344,48825344233129714772,7202552030561982627472,1464587581921220811285325,365627222082497915618219716,125253905685915522767942493032,52893528399758443649956432899616
%N A005164 Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square.
%D A005164 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.
%D A005164 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A005164 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.
%H A005164 C. Hagendorf and J. Liénardy <a href="https://arxiv.org/abs/2008.03220">The open XXZ chain at ∆ = -1/2 and the boundary quantum Knizhnik-Zamolodchikov equations</a>, arXiv:2008.03220 [math-ph], 2020.
%H A005164 D. P. Robbins, <a href="https://arxiv.org/abs/math/0008045">Symmetry classes of alternating sign matrices</a>, arXiv:math/0008045 [math.CO], 2000.
%H A005164 R. P. Stanley, <a href="/A005130/a005130.pdf">A baker's dozen of conjectures concerning plane partitions</a>, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]
%F A005164 Hagendorf and Liénardy give a (conjectured) formula in terms of multiple contour integrals. - _Jean Liénardy_, Aug 15 2020
%Y A005164 Cf. A005130.
%K A005164 nonn,nice,more
%O A005164 0,4
%A A005164 _N. J. A. Sloane_ and _Simon Plouffe_
%E A005164 a(14)-a(19) from _Jean Liénardy_, Aug 15 2020
%E A005164 a(20)-a(24) from _Jean Liénardy_, Sep 21 2022