%I #25 Dec 23 2017 00:11:07

%S 0,0,0,0,240,80400,4012560,76848240,825447840,6005512800,33014872800,

%T 146953113120,554770648080,1835249610480,5448481998960,14778817981200,

%U 37135461679680,87386816771520,194264943433920,410876964198720,831638579799600,1618744884780240

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

%D N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69.

%H Eric M. Schmidt, <a href="/A218514/b218514.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/IcosahedralGraph.html">Icosahedral Graph</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F a(n) = n(n-1)(n-2)(n-3)(n^8 -24n^7 +260n^6 -1670n^5 +6999n^4 -19698n^3 +36408n^2 -40240n +20170).

%F Hence a(n) = n^12 - 30*n^11 + 415*n^10 - 3500*n^9 + 20023*n^8 - 81622*n^7 + 241605*n^6 - 517360*n^5 + 780286*n^4 - 782108*n^3 + 463310*n^2 - 121020*n (cf. A296917) - _N. J. A. Sloane_, Dec 23 2017

%F G.f.: -240*x^4*(12547*x^8 +131518*x^7 +481078*x^6 +743494*x^5 +485740*x^4 +128698*x^3 +12442*x^2 +322*x +1)/(x-1)^13. [_Colin Barker_, Nov 06 2012]

%o (Sage)

%o def A218514(n) : return n*(n-1)*(n-2)*(n-3)*(n^8 -24*n^7 +260*n^6 -1670*n^5 +6999*n^4 -19698*n^3 +36408*n^2 -40240*n +20170);

%o (Maxima)

%o A218514(n):=n*(n-1)*(n-2)*(n-3)*(n^8 -24*n^7 +260*n^6 -1670*n^5 +6999*n^4 -19698*n^3 +36408*n^2 -40240*n +20170)$

%o makelist(A218514(n), n, 0, 30); /* _Martin Ettl_, Nov 03 2012 */

%Y Cf. A052762, A140986, A115400, A218513, A296916, A296917..

%K nonn,easy

%O 0,5

%A _Eric M. Schmidt_, Oct 31 2012