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 A384497 #11 Jun 08 2025 00:07:45
%S A384497 0,0,1,2,6,12,28,56,119,236,479,940,1859,3612,7028,13538,26051,49820,
%T A384497 95098,180774,342944,648648,1224517,2306338,4336449,8138516,15250965,
%U A384497 28535528,53320792,99504804,185474501,345332950,642310142,1193510160,2215702468,4109801864
%N A384497 a(n) is the number of binary strings of length n which contain exactly one run of 1s of even length.
%H A384497 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-6,-2,4,-1).
%F A384497 G.f.: ((1 - x^2) * x^2)/(1 - x - 2 * x^2 + x^3)^2.
%e A384497 a(3)=2 because of the strings 011 and 110.
%t A384497 CoefficientList[Series[((1 - x^2) * x^2)/(1 - x - 2 * x^2 + x^3)^2,{x,0,35}],x] (* _Stefano Spezia_, Jun 02 2025 *)
%Y A384497 Cf. A029907.
%K A384497 nonn,easy
%O A384497 0,4
%A A384497 _Félix Balado_, May 31 2025