A267132 Unipotent n X n matrices over GF(2) that are squares of other such matrices.

1, 1, 22, 316, 85096, 23105944, 87537588832

Offset

1,3

Links

Table of n, a(n) for n=1..7.

Victor S. Miller, Counting Matrices that are Squares, arXiv:1606.09299 [math.GR], 2016.

Formula

a(n)/A002884(n) = sum(lambda,1/C(lambda,2)), where the sum is over all partitions lambda whose conjugate has odd parts with multiplicity <=1 (see A006950), and C(lambda,2) = prod(i>=1,prod(k=0 to m_i(lambda),1-2^(-k))), and m_i(lambda) is the multiplicity of i in the partition lambda (proved).

Example

a(2) = 1, the matrix is [[1,0],[0,1]].

Crossrefs

Cf. A006950 which counts the partitions involved.

Sequence in context: A028231 A326277 A025988 * A023949 A025972 A028029

Adjacent sequences: A267129 A267130 A267131 * A267133 A267134 A267135

Keyword

nonn,more

Author

Victor S. Miller, Jan 13 2016

Status

approved