A287406 Number of direct sum decompositions of a finite vector space of n dimensions over GF(2) whose subspaces are all of distinct dimensions.

1, 1, 1, 29, 121, 10417, 20167393, 1405696961, 1671421144961, 34853495567335169, 18070618208072153366017, 76880583838185587571686401, 5835812465544660559691588302849, 6474896789559157455730381208091095041, 143196455096491413680184647037773197755801601, 76671942287512076984565827384061983641627409659183105

Offset

0,4

Comments

q analog of A007837.

Links

Table of n, a(n) for n=0..15.

David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1

Formula

Sum_{n>=0}a(n)u^n/g(n) = Product_{r>=1}1 + u^r/g(r) where g(n) = A002884(n).

Mathematica

nn = 15; g[n_] := QFactorial[n, q]*(q - 1)^n*q^Binomial[n, 2] /. q -> 2;
Table[g[n], {n, 0, nn}] CoefficientList[Series[Product[1 + u^r/g[r], {r, 1, nn}], {u, 0, nn}], u]

Crossrefs

Sequence in context: A330811 A118614 A033660 * A233114 A264672 A157145

Adjacent sequences: A287403 A287404 A287405 * A287407 A287408 A287409

Keyword

nonn

Author

Geoffrey Critzer, May 24 2017

Status

approved