A054624 Number of ways to color vertices of a 10-gon using <= n colors, allowing only rotations.

0, 1, 108, 5934, 104968, 976887, 6047412, 28249228, 107377488, 348684381, 1000010044, 2593758618, 6191761368, 13785886387, 28925519364, 57665115096, 109951267744, 201599532153, 357046911756, 613106873542, 1024000320168, 1667988506415, 2655992794708

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Row 10 of A075195.

Formula

Sum_{d|10} phi(d)*n^(10/d)/10 = n*(n+1)*(n^8-n^7+n^6-n^5+n^4+4)/10.

G.f.: x*(100*x^8 +4783*x^7 +45547*x^6 +130963*x^5 +131119*x^4 +45469*x^3 +4801*x^2 +97*x+1) / (1-x)^11. - Colin Barker, Jun 12 2012

Extensions

Edited by Christian G. Bower, Sep 07 2002