A140986 Number of n-colorings of the cubical graph.
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
Links
- Eric M. Schmidt, Table of n, a(n) for n = 0..1000
- 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).
Programs
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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
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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 */
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
Extensions
More terms from Alois P. Heinz, Mar 01 2009