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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. 3

%I

%S 0,0,0,9,132,720,2580,7245,17304,36792,71640,130185,223740,367224,

%T 579852,885885,1315440,1905360,2700144,3752937,5126580,6894720,

%U 9142980,11970189,15489672,19830600,25139400,31581225,39341484,48627432,59669820,72724605,88074720

%N 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 Colin Barker, <a href="/A282820/b282820.txt">Table of n, a(n) for n = 0..1000</a>

%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-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12.

%F From _Colin Barker_, Feb 22 2017: (Start)

%F G.f.: 3*x^3*(3 - x)*(1 + 8*x + x^2) / (1 - x)^7.

%F 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 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 Table[(n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12, {n, 0, 32}]

%o (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 (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 Cf. A282817, A282818, A282819, A046023 (tetrahedral edge colorings without restriction).

%K nonn,easy

%O 0,4

%A _David Nacin_, Feb 22 2017

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Last modified October 18 14:04 EDT 2019. Contains 328161 sequences. (Running on oeis4.)