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%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
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