A082963 Number of n X n 0-1 matrices with half 1's and half 0's (rounded up/down if odd).

1, 1, 2, 23, 1674, 652048, 1134460910, 7900674292378, 229078019084673798, 26549036304190836144544, 12611418068196090318131968752, 23955745839516317585042064530077352, 185026624806098273753009169783707528668060

Offset: 0

Author

Vladeta Jovovic, May 27 2003

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• James Grime, Maths Problem: Complete Noughts and Crosses (Burnside's Lemma)

Crossrefs

Cf. A054247, A054252, A014409, A019318.

Programs

PARI

C(n,f)={(f(1)^(n^2) + 2*f(1)^((n%2)*n)*f(2)^((n\2)*n) + 2*f(1)^n*f(2)^binomial(n,2) + f(1)^(n%2)*f(2)^(n^2\2) + 2*f(1)^(n%2)*f(4)^(floor(n/2)*ceil(n/2)))/8}
a(n)={polcoef(C(n, k->1 + x^k), n^2\2)} \\ Andrew Howroyd, Feb 01 2020

Formula

a(n) = A054252(n, floor(n^2/2)).

Extensions

Terms a(12) and beyond from Andrew Howroyd, Feb 01 2020