cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A267132 #29 Jun 13 2021 03:21:22
%S A267132 1,1,22,316,85096,23105944,87537588832
%N A267132 Unipotent n X n matrices over GF(2) that are squares of other such matrices.
%H A267132 Victor S. Miller, <a href="http://arxiv.org/abs/1606.09299">Counting Matrices that are Squares</a>, arXiv:1606.09299 [math.GR], 2016.
%F A267132 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).
%e A267132 a(2) = 1, the matrix is [[1,0],[0,1]].
%Y A267132 Cf. A006950 which counts the partitions involved.
%K A267132 nonn,more
%O A267132 1,3
%A A267132 _Victor S. Miller_, Jan 13 2016