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A218514
Number of n-colorings of the icosahedral graph.
6
0, 0, 0, 0, 240, 80400, 4012560, 76848240, 825447840, 6005512800, 33014872800, 146953113120, 554770648080, 1835249610480, 5448481998960, 14778817981200, 37135461679680, 87386816771520, 194264943433920, 410876964198720, 831638579799600, 1618744884780240
OFFSET
0,5
REFERENCES
N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69.
LINKS
Eric W. Weisstein, Icosahedral Graph
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
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).
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
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]
PROG
(Sage)
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);
(Maxima)
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)$
makelist(A218514(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Oct 31 2012
STATUS
approved