

A005163


Number of alternating sign n X n matrices that are symmetric about a diagonal.
(Formerly M1500)


0



1, 2, 5, 16, 67, 368, 2630, 24376, 293770, 4610624, 94080653, 2492747656, 85827875506, 3842929319936, 223624506056156, 16901839470598576, 1659776507866213636, 211853506422044996288, 35137231473111223912310, 7569998079873075147860464
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OFFSET

1,2


COMMENTS

Robbins's paper does not give a formula for this sequence. On the contrary he states: "Apparently these numbers do not factor into small primes, so a simple product formula seems unlikely. Of course this does not rule out other very simple formulas, but these would be more difficult to discover (let alone prove)." As far as I know no formula is currently known.  Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008


REFERENCES

BousquetMélou, Mireille; and Habsieger, Laurent; Sur les matrices a signes alternants, [On alternatingsign matrices] in Formal power series and algebraic combinatorics (Montreal, PQ, 1992). Discrete Math. 139 (1995), 5772.
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=1..20.
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]


CROSSREFS

Sequence in context: A239912 A239911 A275518 * A006116 A122082 A002631
Adjacent sequences: A005160 A005161 A005162 * A005164 A005165 A005166


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane and Simon Plouffe


EXTENSIONS

More terms (taken from BousquetMélou & Habsieger's paper) from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008


STATUS

approved



