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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). 10

%I

%S 1,1,2,23,1674,652048,1134460910,7900674292378,229078019084673798,

%T 26549036304190836144544,12611418068196090318131968752,

%U 23955745839516317585042064530077352,185026624806098273753009169783707528668060

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

%H Andrew Howroyd, <a href="/A082963/b082963.txt">Table of n, a(n) for n = 0..50</a>

%H James Grime, <a href="http://www.youtube.com/watch?v=wdDF7_vfLcE">Maths Problem: Complete Noughts and Crosses (Burnside's Lemma)</a>

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

%o (PARI)

%o 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 a(n)={polcoef(C(n, k->1 + x^k), n^2\2)} \\ _Andrew Howroyd_, Feb 01 2020

%Y Cf. A054247, A054252, A014409, A019318.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, May 27 2003

%E Terms a(12) and beyond from _Andrew Howroyd_, Feb 01 2020

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)