

A005161


Number of alternating sign 2n+1 X 2n+1 matrices symmetric with respect to both horizontal and vertical axes.
(Formerly M1700)


2



1, 1, 1, 2, 6, 33, 286, 4420, 109820, 4799134, 340879665, 42235307100, 8564558139000
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OFFSET

0,4


REFERENCES

Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.
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..12.
I. Gessel and G. Xin, The generating function of ternary trees and continued fractions
P. Pyatov, Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon. [From Vladeta Jovovic, Aug 15 2008]
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. 285293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]


FORMULA

Robbins gives a simple (conjectured) formula.


CROSSREFS

Sequence in context: A053042 A174432 A012874 * A062970 A259436 A278611
Adjacent sequences: A005158 A005159 A005160 * A005162 A005163 A005164


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms (from the P. Pyatov paper) from Vladeta Jovovic, Aug 15 2008


STATUS

approved



