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

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