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A063842
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Number of colorings of K_4 using at most n colors.
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7
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1, 11, 66, 276, 900, 2451, 5831, 12496, 24651, 45475, 79376, 132276, 211926, 328251, 493725, 723776, 1037221, 1456731, 2009326, 2726900, 3646776, 4812291, 6273411, 8087376, 10319375, 13043251, 16342236, 20309716, 25050026, 30679275, 37326201, 45133056
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OFFSET
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0,2
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COMMENTS
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a(n-1) is the number of unoriented ways to color the edges of a regular tetrahedron with up to n colors.
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LINKS
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FORMULA
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a(n) = (1/4!)*(n^6 + 6*n^5 + 24*n^4 + 56*n^3 + 83*n^2 + 70*n + 24).
G.f.: (1 + 3*x + 7*x^2 + 3*x^3 + x^4)*(1+x)/(1-x)^7. - M. F. Hasler, Jan 19 2012
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MATHEMATICA
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Needs["Combinatorica`"]
Table[Total[Table[CycleIndex[KSubsetGroup[GraphData[{4, k}, "Automorphisms"], GraphData[{4, k}, "EdgeIndices"]], s], {k, 1, 11}]]/.Table[s[i] -> n, {i, 1, 4}], {n, 0, 30}] (* Geoffrey Critzer, Oct 22 2012 *)
CoefficientList[Series[(1 + 3 x + 7 x^2 + 3 x^3 + x^4) (1 + x) / (1 - x)^7, {x, 0, 35}], x] (* Vincenzo Librandi, Jul 21 2013 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 11, 66, 276, 900, 2451, 5831}, 40] (* Harvey P. Dale, Sep 10 2023 *)
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PROG
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(Magma) [1/24*(n^6+6*n^5+24*n^4+56*n^3+83*n^2+70*n+24): n in [0..35]]; // Vincenzo Librandi, Jul 21 2013
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CROSSREFS
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A327084(3,n) = a(n-1) (unoriented simplex edge colorings)
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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