A054620 Number of ways to color vertices of a pentagon using <= n colors, allowing only rotations.

0, 1, 8, 51, 208, 629, 1560, 3367, 6560, 11817, 20008, 32219, 49776, 74269, 107576, 151887, 209728, 283985, 377928, 495235, 640016, 816837, 1030744, 1287287, 1592544, 1953145, 2376296, 2869803, 3442096, 4102253, 4860024

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A060446, A006527, A006528, A006565, A054621, ..., A075195.

Programs

Magma

[(n^5+4*n)/5: n in [0..40]]; // Vincenzo Librandi, Aug 31 2011

Formula

a(n) = (n^5+4*n)/5 = n*(n^2-2*n+2)*(n^2+2*n+2)/5.

G.f.: x*(1+2*x+18*x^2+2*x^3+x^4) / (x-1)^6 . - R. J. Mathar, Aug 30 2011

a(n) = -a(-n). - Bruno Berselli, Aug 31 2011