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A005163 Number of alternating sign n X n matrices that are symmetric about a diagonal.
(Formerly M1500)
1, 2, 5, 16, 67, 368, 2630, 24376, 293770, 4610624, 94080653, 2492747656, 85827875506, 3842929319936, 223624506056156, 16901839470598576, 1659776507866213636, 211853506422044996288, 35137231473111223912310, 7569998079873075147860464 (list; graph; refs; listen; history; text; internal format)



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


Bousquet-Melou, Mireille; and Habsieger, Laurent; Sur les matrices a signes alternants, [On alternating-sign matrices] in Formal power series and algebraic combinatorics (Montreal, PQ, 1992). Discrete Math. 139 (1995), 57-72.

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.


Table of n, a(n) for n=1..20.

D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv:math.CO/0008045


Sequence in context: A019504 A239912 A239911 * A006116 A122082 A002631

Adjacent sequences:  A005160 A005161 A005162 * A005164 A005165 A005166




N. J. A. Sloane and Simon Plouffe


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



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Last modified November 29 12:42 EST 2015. Contains 264646 sequences.