A094813 a(n) = number of (0,1) matrices of size n X n whose determinants are k, where -L <= k <= +L and L = A003432(n).

1, 13, 10, 33, 84, 338, 84, 360, 1200, 10020, 42976, 10020, 12003600, 42795, 145485, 1206772, 4848581, 21059938, 4848585, 1206796, 145473, 42807, 3600

Offset

1,2

Links

Table of n, a(n) for n=1..23.

J. Brenner, The Hadamard maximum determinant problem, Amer. Math. Monthly, 79 (1972), 626-630.

J. Williamson, Determinants whose elements are 0 and 1, Amer. Math. Monthly 53 (1946), 427-434. Math. Rev. 8,128g.

Example

n = 2 : det([a b];[c d]) is (ad - bc) [16 possible matrices]
0 if ((a OR d) = zero) AND ((b OR c) = zero)
OR ((a AND d) = one) AND ((b AND D) = one) [10 possible matrices]
+1 if ((a AND d) = one) AND ((b OR c) = zero) [ 3 possible matrices]
-1 if ((a OR d) = zero) AND ((b AND c) = one) [ 3 possible matrices]

Crossrefs

Cf. A003432, A003433.

Sequence in context: A291425 A180864 A206608 * A364712 A152298 A158956

Adjacent sequences: A094810 A094811 A094812 * A094814 A094815 A094816

Keyword

hard,nonn

Author

Patricia J. Egan (capdevcom(AT)lycos.com), Jun 11 2004

Status

approved