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A286397
Number of inequivalent n X n matrices over an alphabet of size 10 under action of dihedral group of the square D_4.
3
1, 10, 1540, 125512750, 1250002537502500, 1250000000501250002500000, 125000000000000250375000000250000000, 1250000000000000000005001250000000002500000000000
OFFSET
0,2
COMMENTS
Burnside's orbit-counting lemma.
LINKS
M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
María Merino, Imanol Unanue, Yosu Yurramendi, May 08 2017
STATUS
approved