%I #27 Jan 20 2024 14:23:21

%S 0,0,2,114,2652,29660,198030,932862,3440024,10599192,28478970,

%T 68716010,152040372,313269684,608134982,1122341430,1983307440,

%U 3375066032,5556852594,8885943522,13845350540,21077015820,31421193342,45962742254,66085098312,93532729800

%N Number of n-colorings of the cubical graph.

%H Eric M. Schmidt, <a href="/A140986/b140986.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicalGraph.html">Cubical Graph</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

%F a(n) = n^8-12*n^7+66*n^6-214*n^5+441*n^4-572*n^3+423*n^2-133*n.

%F 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

%F a(n) = Sum_{k=1..8} k!*binomial(n,k)*A334159(3,k). - _Andrew Howroyd_, Apr 22 2020

%p a:= n-> n^8 -12*n^7 +66*n^6 -214*n^5 +441*n^4 -572*n^3 +423*n^2 -133*n:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 01 2009

%o (Maxima)

%o A140986(n):=n^8-12*n^7+66*n^6-214*n^5+441*n^4-572*n^3 +423*n^2-133*n$

%o makelist(A140986(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */

%Y Cf. A296914, A334159.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Jul 28 2008

%E More terms from _Alois P. Heinz_, Mar 01 2009