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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
0, 0, 0, 9, 132, 720, 2580, 7245, 17304, 36792, 71640, 130185, 223740, 367224, 579852, 885885, 1315440, 1905360, 2700144, 3752937, 5126580, 6894720, 9142980, 11970189, 15489672, 19830600, 25139400, 31581225, 39341484, 48627432, 59669820, 72724605, 88074720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

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

From Colin Barker, Feb 22 2017: (Start)

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

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)

EXAMPLE

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.

MATHEMATICA

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

PROG

(PARI) a(n) = (n-2)*n*(n-1)*(n^3+3*n^2-10*n-6)/12 \\ Charles R Greathouse IV, Feb 22 2017

(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

CROSSREFS

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

Sequence in context: A200407 A194895 A112123 * A296318 A167253 A097999

Adjacent sequences:  A282817 A282818 A282819 * A282821 A282822 A282823

KEYWORD

nonn,easy

AUTHOR

David Nacin, Feb 22 2017

STATUS

approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)