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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..1000

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

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

Sequence in context: A289636 A001943 A052263 * A270054 A213696 A275459

Adjacent sequences:  A218511 A218512 A218513 * A218515 A218516 A218517

KEYWORD

nonn,easy

AUTHOR

Eric M. Schmidt, Oct 31 2012

STATUS

approved

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Last modified June 25 02:36 EDT 2021. Contains 345449 sequences. (Running on oeis4.)