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 A282819 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. 2

%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*(n-1)*(n^4-2*n^3+n^2+8)/12.

%F G.f.: -2*x^2*(1+4*x+20*x^2+4*x^3+x^4) / (x-1)^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*(n-1)*(n^4-2*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

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Last modified July 19 19:50 EDT 2024. Contains 374436 sequences. (Running on oeis4.)