A393204 Number of n X n matrices over GF(2) such that the row space is equal to the column space.

1, 2, 10, 218, 22906, 10651322, 20802031930, 166437057472058, 5390064106232598586, 702352303362638758749242, 367156773639729499052442504250, 768856023700258389105237851742346298, 6444908708706586437631037608905406860868666

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = Sum_{k=0..n} A002884(k)*A022166(n,k).

Mathematica

nn = 12; B[n_] := QFactorial[n, 2]; e[z_] := Sum[z^n/B[n], {n, 0, nn}]; A[z_] := Sum[Product[2^n - 2^i, {i, 0, n - 1}] z^n/B[n], {n, 0, nn}]; Table[B[n], {n, 0, nn}] CoefficientList[Series[A[z]*e[z], {z, 0, nn}], z]

Crossrefs

Cf. A002884, A022166.

Sequence in context: A001528 A293148 A193482 * A346222 A289948 A282567

Adjacent sequences: A393201 A393202 A393203 * A393205 A393206 A393207

Keyword

nonn

Author

Geoffrey Critzer, Feb 05 2026

Status

approved