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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

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.

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

Adjacent sequences:  A282815 A282816 A282817 * A282819 A282820 A282821

KEYWORD

nonn,easy

AUTHOR

David Nacin, Feb 22 2017

STATUS

approved

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Last modified June 25 06:26 EDT 2019. Contains 324347 sequences. (Running on oeis4.)