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A140986
Number of n-colorings of the cubical graph.
14
0, 0, 2, 114, 2652, 29660, 198030, 932862, 3440024, 10599192, 28478970, 68716010, 152040372, 313269684, 608134982, 1122341430, 1983307440, 3375066032, 5556852594, 8885943522, 13845350540, 21077015820, 31421193342, 45962742254, 66085098312, 93532729800
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Chromatic Polynomial
Eric Weisstein's World of Mathematics, Cubical Graph
Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
FORMULA
a(n) = n^8-12*n^7+66*n^6-214*n^5+441*n^4-572*n^3+423*n^2-133*n.
G.f.: 2*x^2*(1+48*x+849*x^2+4864*x^3+8619*x^4+4848*x^5+931*x^6)/(1-x)^9. - Colin Barker, Apr 15 2012
a(n) = Sum_{k=1..8} k!*binomial(n,k)*A334159(3,k). - Andrew Howroyd, Apr 22 2020
MAPLE
a:= n-> n^8 -12*n^7 +66*n^6 -214*n^5 +441*n^4 -572*n^3 +423*n^2 -133*n:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 01 2009
PROG
(Maxima)
A140986(n):=n^8-12*n^7+66*n^6-214*n^5+441*n^4-572*n^3 +423*n^2-133*n$
makelist(A140986(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
CROSSREFS
Sequence in context: A034312 A224871 A230471 * A157068 A008271 A362575
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jul 28 2008
EXTENSIONS
More terms from Alois P. Heinz, Mar 01 2009
STATUS
approved