This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051170 #27 Sep 08 2022 08:44:59 %S A051170 0,1,3,7,14,25,42,66,99,143,200,273,364,476,612,775,969,1197,1463, %T A051170 1771,2125,2530,2990,3510,4095,4750,5481,6293,7192,8184,9275,10472, %U A051170 11781,13209,14763,16450,18278,20254,22386,24682 %N A051170 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 A051170 G. C. Greubel, <a href="/A051170/b051170.txt">Table of n, a(n) for n = 5..5000</a> %H A051170 <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a> %H A051170 <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 A051170 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 A051170 a(n) = floor(C(n,5)/n). - _Alois P. Heinz_, Jun 05 2013 %F A051170 G.f.: x^5/5 * (1/(1-x)^5 - 1/(1-x^5)). - _Herbert Kociemba_, Oct 16 2016 %t A051170 Table[Floor[Binomial[n, 5]/n], {n, 5, 50}] (* _G. C. Greubel_, Nov 26 2017 *) %o A051170 (PARI) for(n=5,30, print1(floor(binomial(n,5)/n), ", ")) \\ _G. C. Greubel_, Nov 26 2017 %o A051170 (Magma) [ Floor(Binomial(n,5)/n): n in [5..30]]; // _G. C. Greubel_, Nov 26 2017 %Y A051170 Cf. A000031, A001037, A051168. Same as A011795(n-1). %Y A051170 First differences of A036837. %K A051170 nonn,easy %O A051170 5,3 %A A051170 _Clark Kimberling_