A060532 Number of ways to color vertices of a heptagon using <= n colors, allowing rotations and reflections.

0, 1, 18, 198, 1300, 5895, 20646, 60028, 151848, 344925, 719290, 1399266, 2569788, 4496323, 7548750, 12229560, 19206736, 29351673, 43782498, 63913150, 91508580, 128746431, 178285558, 243341748, 327771000, 436160725, 573929226

Offset: 0

Author

N. J. A. Sloane, Apr 12 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Programs

Mathematica

Table[(n^7+7n^4+6n)/14,{n,0,40}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,18,198,1300,5895,20646,60028},40] (* Harvey P. Dale, Aug 15 2016 *)

PARI

{ for (n=0, 200, write("b060532.txt", n, " ", (n^7 + 7*n^4 + 6*n)/14); ) } \\ Harry J. Smith, Jul 06 2009

Formula

a(n) = (n^7+7*n^4+6*n)/14.

G.f.: x*(1+10*x+82*x^2+164*x^3+101*x^4+2*x^5)/(1-x)^8. [Colin Barker, Jan 29 2012]