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A286392 Number of inequivalent n X n matrices over an alphabet of size 6 under action of dihedral group of the square D_4. 7
1, 6, 231, 1284066, 352654485156, 3553786240466361696, 1289303099816839265917858176, 16839193280515921004090301582258640896, 7917535832871659713272867459049024690729209839616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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.

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 *)

CROSSREFS

Column k=6 of A343097.

Cf. A054247, A054739, A054751, A054752.

Sequence in context: A099124 A172862 A099129 * A221926 A324232 A307888

Adjacent sequences:  A286389 A286390 A286391 * A286393 A286394 A286395

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 24 14:36 EDT 2022. Contains 354037 sequences. (Running on oeis4.)