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%I #14 Feb 23 2017 04:37:14
%S 0,0,0,2,20,110,460,1540,4312,10500,22920,45870,85580,150722,252980,
%T 407680,634480,958120,1409232,2025210,2851140,3940790,5357660,7176092,
%U 9482440,12376300,15971800,20398950,25805052,32356170,40238660,49660760,60854240,74076112
%N 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.
%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*(n-1)*(n-2)*(n^3-9*n^2+32*n-38)/12.
%F G.f.: -2*x^3*(1+3*x+6*x^2+20*x^3)/(x-1)^7 . - _R. J. Mathar_, Feb 23 2017
%F a(n) = 2*A249460(n). - _R. J. Mathar_, Feb 23 2017
%e 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.
%t Table[n (n - 1) (n - 2) (n^3 - 9 n^2 + 32 n - 38)/12, {n, 0, 34}]
%o (PARI) a(n) = n*(n-1)*(n-2)*(n^3-9*n^2+32*n-38)/12 \\ _Charles R Greathouse IV_, Feb 22 2017
%Y Cf. A282819, A282820, A046023 (tetrahedral edge colorings without restriction).
%K nonn,easy
%O 0,4
%A _David Nacin_, Feb 22 2017
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