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

0,3

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).

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

Prog

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

Crossrefs

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

Sequence in context: A348594 A078304 A000851 * A034516 A240360 A069325

Adjacent sequences: A054617 A054618 A054619 * A054621 A054622 A054623

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 16 2000

Status

approved