A282820 -id:A282820 - cp's OEIS frontend

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

David Nacin, Feb 22 2017

			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.

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

Cf. A282819, A282820, A046023 (tetrahedral edge colorings without restriction).

Table[n (n - 1) (n - 2) (n^3 - 9 n^2 + 32 n - 38)/12, {n, 0, 34}]

a(n) = n*(n-1)*(n-2)*(n^3-9*n^2+32*n-38)/12 \\ Charles R Greathouse IV, Feb 22 2017

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

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.

Original entry on oeis.org

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

David Nacin, Feb 22 2017

			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.

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

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

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

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

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

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula