A286394 Number of inequivalent n X n matrices over GF(8) under action of dihedral group of the square D_4.

1, 8, 666, 16912512, 35184646816768, 4722366500530551259136, 40564819207305653446303190876160, 22300745198530623151211847196048401987796992, 784637716923335095479473759060307277562325323313332617216

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..33
• M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

Crossrefs

Column k=8 of A343097.

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

Formula

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

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