A286397 Number of inequivalent n X n matrices over an alphabet of size 10 under action of dihedral group of the square D_4.

1, 10, 1540, 125512750, 1250002537502500, 1250000000501250002500000, 125000000000000250375000000250000000, 1250000000000000000005001250000000002500000000000

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..20
• M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

Crossrefs

Column k=10 of A343097.

Cf. A054247, A054739, A054751, A054752, A286392, A286393, A286394, A286395.

Programs

Mathematica

Table[1/8*(10^(n^2) + 2*10^((n^2 + 3 #)/4) + (3 - 2 #)*10^((n^2 + #)/2) + (2 + 2 #)*10^((n^2 + n)/2)) &@ Boole@ OddQ@ n, {n, 7}] (* Michael De Vlieger, May 12 2017 *)

Formula

a(n) = (1/8)*(10^(n^2) + 2*10^(n^2/4) + 3*10^(n^2/2) + 2*10^((n^2 + n)/2)) if n is even;

a(n) = (1/8)*(10^(n^2) + 2*10^((n^2 + 3)/4) + 10^((n^2 + 1)/2) + 4*10^((n^2 + n)/2)) if n is odd.