A282820 Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no color appears more than twice.

0, 0, 0, 9, 132, 720, 2580, 7245, 17304, 36792, 71640, 130185, 223740, 367224, 579852, 885885, 1315440, 1905360, 2700144, 3752937, 5126580, 6894720, 9142980, 11970189, 15489672, 19830600, 25139400, 31581225, 39341484, 48627432, 59669820, 72724605, 88074720

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12.

From Colin Barker, Feb 22 2017: (Start)

G.f.: 3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6. (End)

Example

For n = 3 we get a(3) = 9 ways to color the edges of a tetrahedron in three colors so that no color appears more than twice.

Mathematica

Table[(n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12, {n, 0, 32}]

Prog

(PARI) a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12 \\ Charles R Greathouse IV, Feb 22 2017
(PARI) concat(vector(3), Vec(3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Feb 22 2017

Crossrefs

Cf. A282817, A282818, A282819, A046023 (tetrahedral edge colorings without restriction).

Sequence in context: A200407 A194895 A112123 * A296318 A167253 A366017

Adjacent sequences: A282817 A282818 A282819 * A282821 A282822 A282823

Keyword

nonn,easy

Author

David Nacin, Feb 22 2017

Status

approved