A286393 Number of inequivalent n X n matrices over GF(7) under action of dihedral group of the square D_4.

1, 7, 406, 5105212, 4154189102413, 167633579843887699759, 331466355732596931093508048522, 32115447190132359991237336502881651018804, 152470060954479462517322396167243320349298407119379801

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

Crossrefs

Column k=7 of A343097.

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

Formula

a(n) = (1/8)*(7^(n^2) + 2*7^(n^2/4) + 3*7^(n^2/2) + 2*7^((n^2 + n)/2)) if n is even;

a(n) = (1/8)*(7^(n^2) + 2*7^((n^2 + 3)/4) + 7^((n^2 + 1)/2) + 4*7^((n^2 + n)/2)) if n is odd.