A282818 - OEIS

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.

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

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1)

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.