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 A147611 #18 Oct 25 2022 20:07:20
%S A147611 0,0,0,0,2,7,18,42,84,153,264,429,666,1001,1456,2061,2856,3876,5166,
%T A147611 6783,8778,11214,14168,17710,21924,26910,32760,39582,47502,56637,
%U A147611 67122,79112,92752,108207,125664,145299,167310,191919,219336,249795,283556
%N A147611 The 3rd Witt transform of A000027.
%C A147611 a(n) is the number of binary Lyndon words of length n+3 having 3 blocks of 0's, see Math.SE. - _Andrey Zabolotskiy_, Nov 16 2021
%H A147611 Vincenzo Librandi, <a href="/A147611/b147611.txt">Table of n, a(n) for n = 0..1000</a>
%H A147611 Pieter Moree, <a href="http://dx.doi.org/10.1016/j.disc.2005.03.004">The formal series Witt transform</a>, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.
%H A147611 Pieter Moree, <a href="http://arxiv.org/abs/math/0311205">Convoluted convolved Fibonacci numbers</a>, arXiv:math/0311205 [math.CO].
%H A147611 Felix Pahl, <a href="https://math.stackexchange.com/a/3641671">Find the number of n-length Lyndon words on alphabet {0,1} with k blocks of 0's. (answer)</a>, Mathematics StackExchange, 2020.
%H A147611 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,6,-9,12,-9,6,-6,4,-1).
%F A147611 G.f.: x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2).
%F A147611 a(n) = (1/27)*((3*A049347(n) + A049347(n-1)) - 3*(-1)^n*(A099254(n) - A099254(n- 1)) + n*(3*n^4 - 15*n^2 - 28)/40). - _G. C. Greubel_, Oct 24 2022
%t A147611 CoefficientList[Series[x^4(2 -x+ 2*x^2)/((1-x)^6*(1 +x +x^2)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 13 2012 *)
%o A147611 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0,0,0,0] cat Coefficients(R!( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) )); // _G. C. Greubel_, Oct 24 2022
%o A147611 (SageMath)
%o A147611 def A147611_list(prec):
%o A147611 P.<x> = PowerSeriesRing(ZZ, prec)
%o A147611 return P( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) ).list()
%o A147611 A147611_list(50) # _G. C. Greubel_, Oct 24 2022
%Y A147611 Cf. A006584 (2nd Witt transform of A000027), A049347, A099254, A147618.
%K A147611 easy,nonn
%O A147611 0,5
%A A147611 _R. J. Mathar_, Nov 08 2008