A005160 Number of alternating sign n X n matrices invariant under a quarter turn.

1, 0, 1, 2, 3, 0, 12, 40, 100, 0, 1225, 6860, 28812, 0, 1037232, 9779616

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

Robbins incorrectly gives a(12) = 6460.

References

• 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

• G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001.
• D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv:math/0008045 [math.CO], 2000.
• 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

a(4n) gives A059476.

Formula

Robbins gives a simple (conjectured) formula.