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 A118425 #5 Jul 26 2022 11:57:38 %S A118425 0,0,0,1,4,12,30,68,144,291,568,1080,2012,3688,6672,11941,21180,37284, %T A118425 65210,113420,196320,338375,581040,994416,1696824,2887632,4902240, %U A118425 8304073,14038324,23688636,39905238,67118420,112726512,189072363 %N A118425 Number of binary sequences of length n containing exactly one subsequence 001. %C A118425 With an additional 0 at the beginning, the convolution of A000071 with itself. Column 1 of A118424. %H A118425 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,4,0,-1). %F A118425 G.f.=z^3/(1-2z+z^3)^2. %e A118425 a(4)=4 because we have 0010, 0011, 0001 and 1001. %p A118425 g:=z^3/(1-2*z+z^3)^2: gser:=series(g,z=0,40): seq(coeff(gser,z,n),n=0..38); %Y A118425 Cf. A000071, A118424. %K A118425 nonn %O A118425 0,5 %A A118425 _Emeric Deutsch_, Apr 27 2006