login
Number of ways to color vertices of a pentagon using <= n colors, allowing only rotations.
4

%I #21 Sep 08 2022 08:45:01

%S 0,1,8,51,208,629,1560,3367,6560,11817,20008,32219,49776,74269,107576,

%T 151887,209728,283985,377928,495235,640016,816837,1030744,1287287,

%U 1592544,1953145,2376296,2869803,3442096,4102253,4860024

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

%H Vincenzo Librandi, <a href="/A054620/b054620.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

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

%F G.f.: x*(1+2*x+18*x^2+2*x^3+x^4) / (x-1)^6 . - _R. J. Mathar_, Aug 30 2011

%F a(n) = -a(-n). - _Bruno Berselli_, Aug 31 2011

%o (Magma) [(n^5+4*n)/5: n in [0..40]]; // _Vincenzo Librandi_, Aug 31 2011

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Apr 16 2000