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A282818 Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two adjacent edges have the same color. 2
0, 0, 0, 2, 20, 110, 460, 1540, 4312, 10500, 22920, 45870, 85580, 150722, 252980, 407680, 634480, 958120, 1409232, 2025210, 2851140, 3940790, 5357660, 7176092, 9482440, 12376300, 15971800, 20398950, 25805052, 32356170, 40238660, 49660760, 60854240, 74076112 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = n*(n-1)*(n-2)*(n^3-9*n^2+32*n-38)/12.
G.f.: -2*x^3*(1+3*x+6*x^2+20*x^3)/(x-1)^7 . - R. J. Mathar, Feb 23 2017
a(n) = 2*A249460(n). - R. J. Mathar, Feb 23 2017
EXAMPLE
For n = 3 we get a(3) = 2 distinct ways to color the edges of a tetrahedron with three colors so that no two adjacent edges have the same color.
MATHEMATICA
Table[n (n - 1) (n - 2) (n^3 - 9 n^2 + 32 n - 38)/12, {n, 0, 34}]
PROG
(PARI) a(n) = n*(n-1)*(n-2)*(n^3-9*n^2+32*n-38)/12 \\ Charles R Greathouse IV, Feb 22 2017
CROSSREFS
Cf. A282819, A282820, A046023 (tetrahedral edge colorings without restriction).
Sequence in context: A028477 A073077 A069537 * A001797 A084894 A203238
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 22 2017
STATUS
approved

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Last modified July 13 15:08 EDT 2024. Contains 374284 sequences. (Running on oeis4.)