A071102 Determinant of KK* where K is Kasteleyn-Percus matrix for fool's diamond of order n.

1, 2, 15, 384, 32625, 9085440, 8238791743, 24233379889152

Offset: 1

Author

N. J. A. Sloane, May 28 2002

Keywords

• nonn
• more

References

• J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 27).

Links

• J. Propp, Updated article
• J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics

Crossrefs

Cf. A340166, A340291.

Formula

Conjecture from Seiichi Manyama, Jan 04 2021: (Start)

a(2*n+1) = A340291(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - cos(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).

a(2*n) = 2 * 4^(2*(n-1)) * A340166(n) = 2 * 4^(2*(n-1)*n) * Product_{1<=j,k<=n-1} (1 - cos(j*Pi/(2*n))^2 * cos(k*Pi/(2*n))^2). (End)