%I #12 Feb 23 2017 04:27:43
%S 0,0,2,22,152,680,2270,6202,14672,31152,60810,110990,191752,316472,
%T 502502,771890,1152160,1677152,2387922,3333702,4572920,6174280,
%U 8217902,10796522,14016752,18000400,22885850,28829502,36007272,44616152,54875830,67030370,81349952
%N 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.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,21,35,35,21,7,1).
%F a(n) = n*(n1)*(n^42*n^3+n^2+8)/12.
%F G.f.: 2*x^2*(1+4*x+20*x^2+4*x^3+x^4) / (x1)^7 .  _R. J. Mathar_, Feb 23 2017
%F a(n) = 2*A282816(n).  _R. J. Mathar_, Feb 23 2017
%e 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.
%t Table[(n  1) n (n^4  2 n^3 + n^2 + 8)/12, {n, 0, 33}]
%o (PARI) a(n) = n*(n1)*(n^42*n^3+n^2+8)/12 \\ _Charles R Greathouse IV_, Feb 22 2017
%Y Cf. A282816, A282818, A282820. A046023 (tetrahedral edge colorings without restriction).
%K nonn,easy
%O 0,3
%A _David Nacin_, Feb 22 2017
