cp's OEIS Frontend

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.

%I A282820 #13 Feb 22 2017 10:42:39
%S A282820 0,0,0,9,132,720,2580,7245,17304,36792,71640,130185,223740,367224,
%T A282820 579852,885885,1315440,1905360,2700144,3752937,5126580,6894720,
%U A282820 9142980,11970189,15489672,19830600,25139400,31581225,39341484,48627432,59669820,72724605,88074720
%N 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.
%H A282820 Colin Barker, <a href="/A282820/b282820.txt">Table of n, a(n) for n = 0..1000</a>
%H A282820 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A282820 a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12.
%F A282820 From _Colin Barker_, Feb 22 2017: (Start)
%F A282820 G.f.: 3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7.
%F A282820 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)
%e A282820 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.
%t A282820 Table[(n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12, {n, 0, 32}]
%o A282820 (PARI) a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12 \\ _Charles R Greathouse IV_, Feb 22 2017
%o A282820 (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
%Y A282820 Cf. A282817, A282818, A282819, A046023 (tetrahedral edge colorings without restriction).
%K A282820 nonn,easy
%O A282820 0,4
%A A282820 _David Nacin_, Feb 22 2017