A238796 Symmetric (0,1)-matrices of order n where the numbers of 1's is equal to the order n.

1, 1, 2, 10, 52, 326, 2256, 17102, 139448, 1210582, 11116360, 107154092, 1080800788, 11345351096, 123697222208, 1395340522214, 16260899226608, 195214269203174, 2411419562368344, 30583990129966436, 397876675010548832, 5300483255653341714

Offset

0,3

Comments

For n = 3, we have the following 10 matrices:

1 0 0 1 1 0 1 0 1 1 0 0 0 1 0

0 1 0 1 0 0 0 0 0 0 0 1 1 1 0

0 0 1, 0 0 0, 1 0 0, 0 1 0, 0 0 0,

,

0 0 0 0 0 1 0 1 0 0 0 1 0 0 0

0 1 1 0 1 0 1 0 0 0 0 0 0 0 1

0 1 0, 1 0 0, 0 0 1, 1 0 1, 0 1 1

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = [x^n](1+x)^n*(1+x^2)^binomial(n, 2).

a(n) = sum( binomial(n, 2k)*binomial(binomial(n, 2), k), k=0..n/2 ).

a(n) = sum( binomial(n^2-2k, n-k)*binomial(binomial(n, 2), k)*(-2)^k, k=0..n ).

Mathematica

Table[Sum[Binomial[n, 2k]Binomial[Binomial[n, 2], k], {k, 0, Floor[n/2]}], {n, 0, 100}]

Prog

(Maxima) makelist(sum(binomial(n, 2*k)*binomial(binomial(n, 2), k), k, 0, n/2), n, 0, 20);

Crossrefs

Sequence in context: A074612 A104497 A166694 * A216340 A080117 A080118

Adjacent sequences: A238793 A238794 A238795 * A238797 A238798 A238799

Keyword

nonn

Author

Emanuele Munarini, Mar 05 2014

Status

approved