A290516 Number of diagonalizable n X n matrices over GF(3).

1, 3, 39, 2109, 417153, 346720179, 1233891662727, 17484682043488557, 1077565432934756756289, 290674711165255613845226787, 320439909778519092353160948081831, 1554385919734090411686737202215725913181, 33245671345010828575975932818988836416481765697

Offset: 0

Author

Geoffrey Critzer, Aug 04 2017

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..56
• Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
• Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Crossrefs

Cf. A053290, A132186.

Row sums of A296605.

Programs

Mathematica

nn = 12; g[ n_] := (q - 1)^n q^Binomial[n, 2] FunctionExpand[
    QFactorial[n, q]] /. q -> 3; G[z_] := Sum[z^k/g[k], {k, 0, nn}];Table[g[n], {n, 0, nn}] CoefficientList[Series[G[z]^3, {z, 0, nn}], z]

Formula

a(n)/A053290(n) is the coefficient of x^n in (Sum_{n>=0} x^n/A053290(n))^3.