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 A384155 #10 Jun 04 2025 18:42:16
%S A384155 0,0,0,1,2,3,4,6,11,21,38,65,108,179,299,502,842,1406,2337,3872,6403,
%T A384155 10575,17445,28742,47293,77720,127578,209210,342768,561131,917910,
%U A384155 1500476,2451158,4001723,6529439,10648199,17356589,28278426
%N A384155 a(n) is the number of binary strings of length n whose shortest run of 1s is of length 3.
%H A384155 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,0,-1,-1,1,0,-1).
%F A384155 G.f.: x^3 * (1 - x)^2/(((1 - x)^2 - x^4) * ((1 - x)^2 - x^5)).
%t A384155 LinearRecurrence[{4, -6, 4, 0, -1, -1, 1, 0, -1}, {0, 0, 0, 1, 2, 3, 4, 6, 11}, 50] (* _Amiram Eldar_, May 31 2025 *)
%Y A384155 Cf. A384153, A384154.
%K A384155 nonn,easy
%O A384155 0,5
%A A384155 _Félix Balado_, May 31 2025