A282819 Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two opposite edges have the same color.

0, 0, 2, 22, 152, 680, 2270, 6202, 14672, 31152, 60810, 110990, 191752, 316472, 502502, 771890, 1152160, 1677152, 2387922, 3333702, 4572920, 6174280, 8217902, 10796522, 14016752, 18000400, 22885850, 28829502, 36007272, 44616152, 54875830, 67030370, 81349952

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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

Formula

a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/12.

G.f.: -2*x^2*(1+4*x+20*x^2+4*x^3+x^4) / (x-1)^7 . - R. J. Mathar, Feb 23 2017

a(n) = 2*A282816(n). - R. J. Mathar, Feb 23 2017

Example

For n = 2 we get a(2) = 2 distinct ways to color the edges of a tetrahedron in two colors so that no two opposite edges have the same color.

Mathematica

Table[(n - 1) n (n^4 - 2 n^3 + n^2 + 8)/12, {n, 0, 33}]

Prog

(PARI) a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/12 \\ Charles R Greathouse IV, Feb 22 2017

Crossrefs

Cf. A282816, A282818, A282820. A046023 (tetrahedral edge colorings without restriction).

Sequence in context: A082940 A286778 A232977 * A123960 A265864 A091169

Adjacent sequences: A282816 A282817 A282818 * A282820 A282821 A282822

Keyword

nonn,easy

Author

David Nacin, Feb 22 2017

Status

approved