This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 Bousquet-Mélou, 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. LINKS 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. 285-293 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 EXTENSIONS More terms (taken from Bousquet-Mélou & Habsieger's paper) from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 22 01:35 EST 2019. Contains 320381 sequences. (Running on oeis4.)