A270883 Row sums of triangle A270882. Number of direct-sum decompositions of an n-dimensional vector space over GF(2) with any given nonzero vector in a block.
1, 1, 3, 29, 961, 110657, 45148929, 66294748161, 355213310611457, 7025248750804353025, 517789725632146766102529, 143350189472963401121415823361, 150053549525040193876302690826321921, 597137918840965720442548744290289324130305, 9075744511279922489436849557317778793074029232129
Offset: 0
Keywords
Links
- David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016.
- David Ellerman, The Quantum Logic of Direct-Sum Decompositions, arXiv preprint arXiv:1604.01087 [quant-ph], 2016. See Section 7.5.
Formula
Recurrence: a(n) = Sum_{k=0,...,n-1} q-binomial(n-1,k)*q^(n*(n-k))*D_q(k) where D_q(k) is given by A270881 for q = 2 and where the q-binomial for q = 2 is given by A022166. This summation formula is the q-analog of the summation formula for the Bell numbers A000110 when q = 1. - David P. Ellerman, Mar 26 2016
Extensions
Name edited by David P. Ellerman, Mar 26 2016
a(8)-a(14) from Geoffrey Critzer, May 21 2017