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 A131283 #10 May 30 2020 13:54:15 %S A131283 0,0,1,5,16,38,85,185,396,838,1748,3609,7400,15097,30681,62154,125588, %T A131283 253246,509850,1025153,2059159,4132679,8288643,16615051,33291367, %U A131283 66682128,133525499,267312553,535049374,1070786975,2142690382 %N A131283 a(n) is the number of binary strings of length n such that there exist 3 or more ones in a subsequence of length 5 or less. %H A131283 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1,-2,2,-4,0,-1,2,-1,2). %F A131283 a(n) = 2^n - A120118(n). %F A131283 a(n)= +3*a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) +2*a(n-5) -4*a(n-6) -a(n-8) +2*a(n-9) -a(n-10) +2*a(n-11). %F A131283 G.f.: x^3*(1 +2*x +3*x^2 -x^6 -x^7 -x^3 -2*x^5) / ( (1-2*x)*(1-x-x^3-2*x^5+x^8+x^10) ). - _R. J. Mathar_, Nov 28 2011 %o A131283 (PARI) concat([0, 0], Vec(x^3*(1+2*x+3*x^2-x^6-x^7-x^3-2*x^5) / ( (1-2*x)*(1-x-x^3-2*x^5+x^8+x^10) ) + O(x^40))) \\ _Michel Marcus_, May 28 2020 %Y A131283 Cf. A118646, A118647. %K A131283 nonn,easy %O A131283 1,4 %A A131283 _Tanya Khovanova_, Sep 28 2007