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A286396
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Number of inequivalent n X n matrices over GF(9) under action of dihedral group of the square D_4.
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3
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1, 9, 1035, 48700845, 231628411446741, 89737248564744874067889, 2816049943117424212512789695666175, 7158021121277935153545945911617993395398302485, 1473773072217322896440109113309952350877179744639518847951721
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OFFSET
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0,2
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COMMENTS
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Burnside's orbit-counting lemma.
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LINKS
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María Merino, Table of n, a(n) for n = 0..32
M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).
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FORMULA
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a(n) = (1/8)*(9^(n^2) + 2*9^(n^2/4) + 3*9^(n^2/2) + 2*9^((n^2 + n)/2)) if n is even;
a(n) = (1/8)*(9^(n^2) + 2*9^((n^2 + 3)/4) + 9^((n^2 + 1)/2) + 4*9^((n^2 + n)/2)) if n is odd.
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MATHEMATICA
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Table[1/8*(9^(n^2) + 2*9^((n^2 + 3 #)/4) + (3 - 2 #)*9^((n^2 + #)/2) + (2 + 2 #)*9^((n^2 + n)/2)) &@ Boole@ OddQ@ n, {n, 0, 7}] (* Michael De Vlieger, May 12 2017 *)
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CROSSREFS
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Column k=9 of A343097.
Cf. A054247, A054739, A054751, A054752, A286392, A286393, A286394.
Sequence in context: A099127 A172944 A277829 * A174636 A054344 A048912
Adjacent sequences: A286393 A286394 A286395 * A286397 A286398 A286399
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KEYWORD
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nonn
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AUTHOR
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María Merino, Imanol Unanue, Yosu Yurramendi, May 08 2017
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STATUS
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approved
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