A060561 Number of ways to color vertices of a 9-gon using <= n colors, allowing rotations and reflections.

0, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969, 55605670, 131077771, 286779076, 589324749, 1148105154, 2136122255, 3818273456, 6588925841, 11020906014, 17928333139, 28446045340, 44128712341, 67073090106

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