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 A386250 #26 Aug 19 2025 16:58:19
%S A386250 0,0,0,0,4,13,36,92,224,528,1216,2752,6144,13568,29696,64512,139264,
%T A386250 299008,638976,1359872,2883584,6094848,12845056,27000832,56623104,
%U A386250 118489088,247463936,515899392,1073741824,2231369728,4630511616,9596567552,19864223744,41070624768,84825604096,175019917312
%N A386250 Total number of ones in runs of 1's of length >= 4 over all binary strings of length n.
%H A386250 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A386250 For n>=4, a(n) = (5*n-12)*2^(n-5).
%F A386250 G.f.: -x^4*(3*x-4)/(2*x-1)^2. - _Alois P. Heinz_, Aug 14 2025
%e A386250 For n=6 there are eight binary strings that contain runs of 1s of length >= 4: 001111, 011110, 011111, 101111, 111100, 111101, 111110 and 111111; the runs of length >= 4 in these strings contain a(6) = 36 ones.
%t A386250 LinearRecurrence [{4,-4}, {4,13}, 30] (* _Hugo Pfoertner_, Aug 14 2025 *)
%Y A386250 Cf. A001787, A066373, A128135, A053220.
%K A386250 nonn,easy
%O A386250 0,5
%A A386250 _Félix Balado_, Aug 14 2025