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A282820
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Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no color appears more than twice.
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3
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0, 0, 0, 9, 132, 720, 2580, 7245, 17304, 36792, 71640, 130185, 223740, 367224, 579852, 885885, 1315440, 1905360, 2700144, 3752937, 5126580, 6894720, 9142980, 11970189, 15489672, 19830600, 25139400, 31581225, 39341484, 48627432, 59669820, 72724605, 88074720
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12.
G.f.: 3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6. (End)
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EXAMPLE
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For n = 3 we get a(3) = 9 ways to color the edges of a tetrahedron in three colors so that no color appears more than twice.
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MATHEMATICA
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Table[(n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12, {n, 0, 32}]
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PROG
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(PARI) concat(vector(3), Vec(3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Feb 22 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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