A286392 Number of inequivalent n X n matrices over an alphabet of size 6 under action of dihedral group of the square D_4.

1, 6, 231, 1284066, 352654485156, 3553786240466361696, 1289303099816839265917858176, 16839193280515921004090301582258640896, 7917535832871659713272867459049024690729209839616

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Computed using Burnside's orbit-counting lemma.

Links

• María Merino, Table of n, a(n) for n = 0..35
• M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

Crossrefs

Column k=6 of A343097.

Cf. A054247, A054739, A054751, A054752.

Programs

Mathematica

Table[1/8*(6^(n^2) + 2*6^((n^2 + 3 #)/4) + (3 - 2 #)*6^((n^2 + #)/2) + (2 + 2 #)*6^((n^2 + n)/2)) &@ Boole[OddQ@ n], {n, 10}] (* Michael De Vlieger, May 08 2017 *)

Formula

a(n) = (1/8)*(6^(n^2) + 2*6^(n^2/4) + 3*6^(n^2/2) + 2*6^((n^2 + n)/2)) if n is even;

a(n) = (1/8)*(6^(n^2) + 2*6^((n^2 + 3)/4) + 6^((n^2 + 1)/2) + 4*6^((n^2 + n)/2)) if n is odd.