A221976 The number of n X n matrices with zero determinant and with entries a permutation of [1,2,..,n^2].

0, 0, 2736, 8290316160

Offset

1,3

Comments

This counts a subset of all (n^2)! = A088020(n) matrices which contain elements which are a permutation of [n^2]. The range of determinants is characterized in A085000, and the size of the set of different determinants in A088217.

Because any combination of row and column permutation of matrices with distinct elements generates (n!)^2 = A001044(n) different matrices, and because these restricted permutations leave the (absolute value of) the determinant constant, a(n) is a multiple of A001044(n). This factor does not yet take into account that matrix transpositions also maintain the values of determinants (and which never can be achieved by row or column permutation).

Links

Table of n, a(n) for n=1..4.

Formula

a(n) = A136609(n)*A001044(n).

Crossrefs

Sequence in context: A253994 A253987 A258904 * A337625 A094401 A035774

Adjacent sequences: A221973 A221974 A221975 * A221977 A221978 A221979

Keyword

hard,nonn,more,bref

Author

R. J. Mathar, May 12 2013

Status

approved