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

Author

Victor S. Miller, Jan 13 2016

Keywords

• nonn
• more

Examples

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

Links

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

Crossrefs

Cf. A006950 which counts the partitions involved.

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).