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

0,3

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).

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]

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 *)

Prog

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

Crossrefs

Sequence in context: A042940 A264356 A034727 * A073397 A020920 A083812

Adjacent sequences: A060529 A060530 A060531 * A060533 A060534 A060535

Keyword

nonn

Author

N. J. A. Sloane, Apr 12 2001

Status

approved