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 A296953 #20 Dec 22 2018 16:10:28
%S A296953 0,1,4,10,22,46,94,190,382,766,1534,3070,6142,12286,24574,49150,98302,
%T A296953 196606,393214,786430,1572862,3145726,6291454,12582910,25165822,
%U A296953 50331646,100663294,201326590,402653182,805306366,1610612734,3221225470,6442450942,12884901886
%N A296953 Number of bisymmetric, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n}.
%C A296953 Apart from the offset the same as A033484. - _R. J. Mathar_, _Alois P. Heinz_, Jan 02 2018
%H A296953 J. Devillet, <a href="https://arxiv.org/abs/1712.07856">Bisymmetric and quasitrivial operations: characterizations and enumerations</a>, arXiv:1712.07856 [math.RA] (2017).
%H A296953 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A296953 a(0)=0, a(1)=1, a(n+1)-2*a(n) = 2.
%F A296953 From _Colin Barker_, Dec 22 2017: (Start)
%F A296953 G.f.: x*(1 + x) / ((1 - x)*(1 - 2*x)).
%F A296953 a(n) = 3*2^(n-1) - 2 for n>0.
%F A296953 a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A296953 (End)
%t A296953 Nest[Append[#, 2 Last@ # + 2] &, {0, 1}, 32] (* or *)
%t A296953 Array[3*2^(# - 1) - 2 + Boole[# == 0]/2 &, 34, 0] (* or *)
%t A296953 CoefficientList[Series[x (1 + x)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* _Michael De Vlieger_, Dec 22 2017 *)
%o A296953 (PARI) concat(0, Vec(x*(1 + x) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ _Colin Barker_, Dec 22 2017
%K A296953 nonn,easy
%O A296953 0,3
%A A296953 _J. Devillet_, Dec 22 2017
%E A296953 G.f. replaced by a better g.f. by _Colin Barker_, Dec 23 2017