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 A347017 #16 Sep 02 2023 16:15:09
%S A347017 1,1,2,4,7,12,22,44,93,200,428,904,1883,3876,7906,16020,32313,64976,
%T A347017 130392,261328,523319,1047436,2095822,4192764,8386837,16775192,
%U A347017 33552132,67106264,134214803,268432180,536867258,1073737764,2147479153,4294962336,8589929136,17179863200,34359731823
%N A347017 a(n) = floor(2^(n-1)) - binomial(n,3) + binomial(n,2) - n + 1.
%C A347017 a(n) is the number of binary strings of length n that contain none, two, five, or a larger odd number of 0's.
%H A347017 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F A347017 E.g.f.: exp(x)*(sinh(x) + 1 - x + x^2/2 - x^3/6).
%F A347017 From _Stefano Spezia_, Aug 11 2021: (Start)
%F A347017 O.g.f.: (1 - 5*x + 10*x^2 - 10*x^3 + 4*x^4 + x^5)/((1 - x)^4*(1 - 2*x)).
%F A347017 a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5) for n > 5. (End)
%e A347017 a(6)=22 since the strings are the 15 permutations of 001111, the 6 permutations of 000001, and 111111.
%t A347017 Table[Floor[2^(n-1)]-Binomial[n,3]+Binomial[n,2]-n+1,{n,0,40}] (* or *) LinearRecurrence[{6,-14,16,-9,2},{1,1,2,4,7,12},40] (* _Harvey P. Dale_, Sep 02 2023 *)
%Y A347017 Cf. A002664, A342379, A342380.
%K A347017 nonn,easy
%O A347017 0,3
%A A347017 _Enrique Navarrete_, Aug 10 2021