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A054751
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Number of inequivalent n X n matrices over GF(4) under action of dihedral group of the square D_4.
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9
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1, 4, 55, 34960, 537157696, 140738033618944, 590295811483987148800, 39614081257168338331296071680, 42535295865117309120430975675097153536, 730750818665451459102461990840694008379514814464, 200867255532373784442745261867639247948787687313041365401600
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 1/8*(4^(n^2) + 2*4^(n^2/4) + 3*4^(n^2/2) + 2*4^((n^2+n)/2)) if n is even;
a(n) = 1/8*(4^(n^2) + 2*4^((n^2+3)/4) + 4^((n^2+1)/2) + 4*4^((n^2+n)/2)) if n is odd.
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MATHEMATICA
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Table[If[EvenQ[n], (4^n^2+2*4^(n^2/4)+3*4^(n^2/2)+2*4^((n^2+n)/2))/8, (4^n^2+2*4^((n^2+3)/4)+4^((n^2+1)/2)+4*4^((n^2+n)/2))/8], {n, 0, 10}] (* Harvey P. Dale, Aug 16 2021 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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