A296918 -id:A296918 - cp's OEIS frontend

A218513 Number of n-colorings of the dodecahedral graph.

0, 0, 0, 7200, 168506880, 112603286160, 15108392957760, 775405390866960, 20886647215714560, 353998543659193440, 4231366997071432320, 38508081275604409920, 281586666065022616320, 1720887594454493527920, 9053942417801770507200, 41955877772610102690480

Offset: 0

Eric M. Schmidt, Oct 31 2012

N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See pp. 69-70.

Eric M. Schmidt, Table of n, a(n) for n = 0..1000
Eric W. Weisstein, Dodecahedral Graph
Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

Cf. A052762, A140986, A115400, A218514, A296918, A296919.

A218513(n):=n*(n-1)*(n-2)*(n^17 -27*n^16 +352*n^15 -2950*n^14 +17839*n^13 -82777*n^12 +305866*n^11 -921448*n^10 +2297495*n^9 -4783425*n^8 +8347700*n^7 -12195590*n^6 +14808795*n^5 -14713381*n^4 +11613602*n^3 -6892084*n^2 +2751604*n -555984)$
makelist(A218513(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */

def A218513(n) : return n*(n-1)*(n-2)*(n^17 -27*n^16 +352*n^15 -2950*n^14 +17839*n^13 -82777*n^12 +305866*n^11 -921448*n^10 +2297495*n^9 -4783425*n^8 +8347700*n^7 -12195590*n^6 +14808795*n^5 -14713381*n^4 +11613602*n^3 -6892084*n^2 +2751604*n -555984);

a(n) = n(n-1)(n-2)(n^17 - 27n^16 + 352n^15 - 2950n^14 + 17839n^13 - 82777n^12 + 305866n^11 - 921448n^10 + 2297495n^9 - 4783425n^8 + 8347700n^7 - 12195590n^6 + 14808795n^5 - 14713381n^4 + 11613602n^3 - 6892084n^2 + 2751604n - 555984).
See A296919 for the coefficients of the expanded form of a(n). - N. J. A. Sloane, Dec 23 2017
G.f.: -240*x^3*(2007273*x^17 +678113783*x^16 +62897280675*x^15 +2149103163405*x^14 +32571452423195*x^13 +246267894384141*x^12 +1000326687571911*x^11 +2283861589692665*x^10 +3002531231655465*x^9 +2288662487004975*x^8 +1001857651156729*x^7 +244960098705399*x^6 +31779760521705*x^5 +2006465657455*x^4 +53246253405*x^3 +454442307*x^2 +701482*x +30)/(x-1)^21. - Colin Barker, Nov 06 2012

A296919 List of coefficients of chromatic polynomial of dodecahedron, highest order terms first.

Original entry on oeis.org

1, -30, 435, -4060, 27393, -142194, 589875, -2004600, 5673571, -13518806, 27292965, -46805540, 68090965, -83530946, 85371335, -71159652, 46655060, -22594964, 7171160, -1111968, 0

Offset: 1

N. J. A. Sloane, Dec 23 2017

sign

This is based on A218513, not on the expression at the top of page 70 of the Biggs reference, which I could not get to work.

			The chromatic polynomial is x^20 - 30*x^19 + 435*x^18 - 4060*x^17 + 27393*x^16 - 142194*x^15 + 589875*x^14 - 2004600*x^13 + 5673571*x^12 - 13518806*x^11 + 27292965*x^10 - 46805540*x^9 + 68090965*x^8 - 83530946*x^7 + 85371335*x^6 - 71159652*x^5 + 46655060*x^4 - 22594964*x^3 + 7171160*x^2 - 1111968*x.

N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69-70.

Cf. A218513, A218514, A296918.

cp's OEIS Frontend

A218513 Number of n-colorings of the dodecahedral graph.

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