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A071102 Determinant of KK* where K is Kasteleyn-Percus matrix for fool's diamond of order n. 0

%I

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

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

%D 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).

%H J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>

%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>

%F Conjecture from _Seiichi Manyama_, Jan 04 2021: (Start)

%F 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).

%F 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)

%Y Cf. A340166, A340291.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, May 28 2002

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Last modified May 15 12:36 EDT 2021. Contains 343917 sequences. (Running on oeis4.)