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A282613
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Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations.
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13
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0, 1, 140, 4995, 65824, 489125, 2521476, 10092775, 33562880, 96870249, 250025500, 589527851, 1290008160, 2651218765, 5165397524, 9611031375, 17180133376, 29647326545, 49590297900, 80672546899, 128000804000, 198571037301, 301818598180, 450289780535
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OFFSET
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0,3
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COMMENTS
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Cycle index of symmetry group (cyclic rotation group of order 4 acting on the 9 cells of the square) is (2s(4)^2*s(1) + s(2)^4*s(1) + s(1)^9)/4.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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a(n) = n^3*(n^2+1)*(n^4-n^2+2)/4.
G.f.: x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10. - Colin Barker, Feb 23 2017
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EXAMPLE
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The number of 3 X 3 binary matrices up to rotations is 140.
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MATHEMATICA
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Table[(2n^3+n^5+n^9)/4, {n, 0, 24}]
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PROG
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(PARI) concat(0, Vec(x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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