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A060561 Number of ways to color vertices of a 9-gon using <= n colors, allowing rotations and reflections. 1
0, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969, 55605670, 131077771, 286779076, 589324749, 1148105154, 2136122255, 3818273456, 6588925841, 11020906014, 17928333139, 28446045340, 44128712341, 67073090106 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..500

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

FORMULA

a(n) = (n^9 + 9*n^5 + 2*n^3 + 6*n)/18.

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), a(0)=0, a(1)=1, a(2)=46, a(3)=1219, a(4)=15084, a(5)=110085, a(6)=563786, a(7)=2250311, a(8)=7472984, a(9)=21552969. - Harvey P. Dale, Nov 23 2011

G.f.: x*(1 + 36*x + 804*x^2 + 4844*x^3 + 8790*x^4 + 4844*x^5 + 804*x^6 + 36*x^7 + x^8)/(1-x)^10. - Colin Barker, Jan 29 2012

MATHEMATICA

Table[(n^9+9n^5+2n^3+6*n)/18, {n, 0, 30}] (* or *) LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969}, 30] (* Harvey P. Dale, Nov 23 2011 *)

PROG

(PARI) a(n)={(n^9 + 9*n^5 + 2*n^3 + 6*n)/18} \\ Harry J. Smith, Jul 07 2009

CROSSREFS

Sequence in context: A211835 A333066 A261940 * A281321 A188412 A066403

Adjacent sequences:  A060558 A060559 A060560 * A060562 A060563 A060564

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 12 2001

STATUS

approved

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Last modified January 27 14:29 EST 2021. Contains 340467 sequences. (Running on oeis4.)