A363351 Number of n element multisets of length n vectors over GF(2) that sum to zero.

1, 1, 4, 15, 276, 11781, 1878976, 1025425687, 1991615557152, 13956142211859705, 356420795746828010496, 33403125520521519582574755, 11550847036800645994553295682560, 14809214844165378046279886451931058885, 70706990798105074752791720424861516970573824

Offset: 0

Author

Andrew Howroyd, May 30 2023

Keywords

• nonn

Comments

Number of equivalence classes of n X n binary matrices with an even number of 1's in each column under permutation of rows.

Number of equivalence classes of n X n binary matrices under permutation of rows and complementation of columns.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Main diagonal of A362905.

Cf. A006383.

Programs

Mathematica

A363351[n_]:=(Binomial[2^n+n-1,n]+If[EvenQ[n],(2^n-1)Binomial[2^(n-1)+n/2-1,n/2],0])/2^n;Array[A363351,20,0] (* Paolo Xausa, Nov 19 2023 *)

PARI

a(n)={(binomial(2^n+n-1, n) + if(n%2==0, (2^n-1)*binomial(2^(n-1)+n/2-1, n/2)))/2^n}

Formula

a(n) = binomial(2^n+n-1, n)/2^n for odd n;

a(n) = (binomial(2^n+n-1, n) + (2^n-1)*binomial(2^(n-1)+n/2-1, n/2))/2^n for even n.