A286396 Number of inequivalent n X n matrices over GF(9) under action of dihedral group of the square D_4.

1, 9, 1035, 48700845, 231628411446741, 89737248564744874067889, 2816049943117424212512789695666175, 7158021121277935153545945911617993395398302485, 1473773072217322896440109113309952350877179744639518847951721

Offset: 0

Author

María Merino, Imanol Unanue, Yosu Yurramendi, May 08 2017

Keywords

• nonn

Comments

Burnside's orbit-counting lemma.

Links

• María Merino, Table of n, a(n) for n = 0..32
• M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

Crossrefs

Column k=9 of A343097.

Cf. A054247, A054739, A054751, A054752, A286392, A286393, A286394.

Programs

Mathematica

Table[1/8*(9^(n^2) + 2*9^((n^2 + 3 #)/4) + (3 - 2 #)*9^((n^2 + #)/2) + (2 + 2 #)*9^((n^2 + n)/2)) &@ Boole@ OddQ@ n, {n, 0, 7}] (* Michael De Vlieger, May 12 2017 *)

Formula

a(n) = (1/8)*(9^(n^2) + 2*9^(n^2/4) + 3*9^(n^2/2) + 2*9^((n^2 + n)/2)) if n is even;

a(n) = (1/8)*(9^(n^2) + 2*9^((n^2 + 3)/4) + 9^((n^2 + 1)/2) + 4*9^((n^2 + n)/2)) if n is odd.