A289543 Number of direct sum decompositions of GF(2)^n that do not contain any subspaces of dimension 1.

1, 0, 1, 1, 281, 9921, 16078337, 13596908545, 191426147495937, 3273234077014474753, 497324772153177747947521, 154709087482207635347155451905, 291534668371237082293312814285062145, 1534814232386517133354150755522868689240065, 39269743760371912650589750432327799926355436503041, 3338607968166762847572429548161284663670177988768356630529

Offset: 0

Author

Geoffrey Critzer, Jul 19 2017

Keywords

• nonn

Comments

q-analog of A000296.

Links

• 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

Crossrefs

Cf. A270881, A287406.

Programs

Mathematica

nn = 15; q := 2; g[n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[QFactorial[n, q]]; G[z_] :=Sum[z^k/g[k], {k, 1, nn}];Table[g[n], {n, 0, nn}] CoefficientList[
  Series[Exp[G[z] - z], {z, 0, nn}], z]

Formula

a(n)/A002884(n) is the coefficient of x^n in the expansion of exp(Sum_{k>1}x^k/A002884(k)).