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%I #27 Sep 08 2022 08:44:59
%S 0,1,3,7,14,25,42,66,99,143,200,273,364,476,612,775,969,1197,1463,
%T 1771,2125,2530,2990,3510,4095,4750,5481,6293,7192,8184,9275,10472,
%U 11781,13209,14763,16450,18278,20254,22386,24682
%N T(n,5), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 5 black beads and n-5 white beads.
%H G. C. Greubel, <a href="/A051170/b051170.txt">Table of n, a(n) for n = 5..5000</a>
%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,1,-4,6,-4,1).
%F G.f.: -x^6*(x^2-x+1) / ((x-1)^5*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Jun 05 2013
%F a(n) = floor(C(n,5)/n). - _Alois P. Heinz_, Jun 05 2013
%F G.f.: x^5/5 * (1/(1-x)^5 - 1/(1-x^5)). - _Herbert Kociemba_, Oct 16 2016
%t Table[Floor[Binomial[n, 5]/n], {n, 5, 50}] (* _G. C. Greubel_, Nov 26 2017 *)
%o (PARI) for(n=5,30, print1(floor(binomial(n,5)/n), ", ")) \\ _G. C. Greubel_, Nov 26 2017
%o (Magma) [ Floor(Binomial(n,5)/n): n in [5..30]]; // _G. C. Greubel_, Nov 26 2017
%Y Cf. A000031, A001037, A051168. Same as A011795(n-1).
%Y First differences of A036837.
%K nonn,easy
%O 5,3
%A _Clark Kimberling_
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