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
Examples
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.
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).
Programs
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Mathematica
Table[(n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12, {n, 0, 32}] -
PARI
a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12 \\ Charles R Greathouse IV, Feb 22 2017
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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
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)