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 A384154 #15 Jun 24 2025 16:10:24
%S A384154 0,0,1,2,3,5,10,20,38,70,128,234,427,776,1404,2531,4550,8161,14608,
%T A384154 26099,46550,82901,147441,261913,464759,823902,1459287,2582615,
%U A384154 4567357,8072082,14257631,25169443,44410452,78325112,138082349,243339192,428683436,754961473
%N A384154 a(n) is the number of binary strings of length n whose shortest run of 1s is of length 2.
%H A384154 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-2,-1,1,-1).
%F A384154 G.f.: x^2 * (1 - x)^2/(((1 - x)^2 - x^3) * ((1 - x)^2 - x^4)).
%t A384154 LinearRecurrence[{4,-6,5,-2,-1,1,-1},{0,0,1,2,3,5,10},40] (* _Harvey P. Dale_, Jun 24 2025 *)
%Y A384154 Cf. A000100, A384153.
%K A384154 nonn,easy
%O A384154 0,4
%A A384154 _Félix Balado_, May 20 2025