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A054623 Number of ways to color vertices of a 9-gon using <= n colors, allowing only rotations. 2
0, 1, 60, 2195, 29144, 217045, 1119796, 4483815, 14913200, 43046889, 111111340, 261994491, 573309320, 1178278205, 2295672484, 4271485135, 7635498336, 13176431825, 22039922460, 35854190179, 56888890680, 88253340581, 134141026580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Length-9 necklaces with n kinds of beads. [Vincenzo Librandi, Apr 29 2012]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

a(n) = Sum_{d|9} phi(d)*n^(9/d)/9.

a(n) = n*(n^8+2*n^2+6)/9.

G.f.: x*(1+50*x+1640*x^2+9774*x^3+17390*x^4+9774*x^5+1640*x^6+50*x^7+x^8)/ (1-x)^10. [Colin Barker, Jan 29 2012]

a(n) = 10*a(n-1) -45*a(n-2) +120*a(n-3) -210*a(n-4)+252*a(n-5) -210*a(n-6) +120*a(n-7) -45*a(n-8) +10*a(n-9) -a(n-10). [Vincenzo Librandi, Apr 29 2012]

MATHEMATICA

CoefficientList[Series[x*(1+50*x+1640*x^2+9774*x^3+17390*x^4+9774*x^5+1640*x^6+50*x^7+x^8)/(1-x)^10, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 29 2012 *)

PROG

(MAGMA) [n*(n^8+2*n^2+6)/9: n in [0..30]]; // Vincenzo Librandi, Apr 30 2012

CROSSREFS

Row 9 of A075195.

Sequence in context: A004353 A269284 A004364 * A075908 A130647 A062263

Adjacent sequences:  A054620 A054621 A054622 * A054624 A054625 A054626

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 16 2000

EXTENSIONS

Edited by Christian G. Bower, Sep 07 2002

STATUS

approved

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)