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

%I A082963 #19 Apr 05 2020 20:12:18
%S A082963 1,1,2,23,1674,652048,1134460910,7900674292378,229078019084673798,
%T A082963 26549036304190836144544,12611418068196090318131968752,
%U A082963 23955745839516317585042064530077352,185026624806098273753009169783707528668060
%N A082963 Number of n X n 0-1 matrices with half 1's and half 0's (rounded up/down if odd).
%H A082963 Andrew Howroyd, <a href="/A082963/b082963.txt">Table of n, a(n) for n = 0..50</a>
%H A082963 James Grime, <a href="http://www.youtube.com/watch?v=wdDF7_vfLcE">Maths Problem: Complete Noughts and Crosses (Burnside's Lemma)</a>
%F A082963 a(n) = A054252(n, floor(n^2/2)).
%o A082963 (PARI)
%o A082963 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}
%o A082963 a(n)={polcoef(C(n, k->1 + x^k), n^2\2)} \\ _Andrew Howroyd_, Feb 01 2020
%Y A082963 Cf. A054247, A054252, A014409, A019318.
%K A082963 nonn
%O A082963 0,3
%A A082963 _Vladeta Jovovic_, May 27 2003
%E A082963 Terms a(12) and beyond from _Andrew Howroyd_, Feb 01 2020