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.
a(n) counts the nodes in generation n of the following tree. Generations 0..5 of the 2-convoluted tree are as follows; The path from the root is shown, with child nodes enclosed in []. GEN.0: [1]; GEN.1: 1->[2]; GEN.2: 1-2->[1,3]; GEN.3: 1-2-1->[2] 1-2-3->[2,4,6]; GEN.4: 1-2-1-2->[2,4] 1-2-3-2->[1,3] 1-2-3-4->[1,3,5,7] 1-2-3-6->[1,3,5,7,9,11]; GEN.5: 1-2-1-2-2->[2,4] 1-2-1-2-4->[2,4,6,8] 1-2-3-2-1->[2] 1-2-3-2-3->[2,4,6] 1-2-3-4-1->[2] 1-2-3-4-3->[2,4,6] 1-2-3-4-5->[2,4,6,8,10] 1-2-3-4-7->[2,4,6,8,10,12,14] 1-2-3-6-1->[2] 1-2-3-6-3->[2,4,6] 1-2-3-6-5->[2,4,6,8,10] 1-2-3-6-7->[2,4,6,8,10,12,14] 1-2-3-6-9->[2,4,6,8,10,12,14,16,18] 1-2-3-6-11->[2,4,6,8,10,12,14,16,18,20,22]. Each path in the tree from the root node forms the initial terms of a self-convolution square of a sequence with integer terms.
{a(n)=local(B=[1],R);if(n==0,1,for(k=1,n,t=3*a(k-1);B=concat(B,t); R=Vec(Ser(B)^(1/3))[ #B]; B[ #B]=t-(numerator(R)%3)*(denominator(R)-1)/2 ));B[n+1]}
{a(n)=local(A,t,r=1);A=if(n==0,[1],vector(n,j,a(j-1)));if(n==0,r=1,t=a(n-1); if(denominator(Vec(Ser(concat(A,4*t))^(1/4))[n+1])==1,r=4*t, if(denominator(Vec(Ser(concat(A,4*t-1))^(1/4))[n+1])==1,r=4*t-1, if(denominator(Vec(Ser(concat(A,4*t-2))^(1/4))[n+1])==1,r=4*t-2,r=4*t-3))));r}
{a(n)=local(A,t,r=1);A=if(n==0,[1],vector(n,j,a(j-1)));if(n==0,r=1,t=a(n-1); if(denominator(Vec(Ser(concat(A,5*t))^(1/5))[n+1])==1,r=5*t, if(denominator(Vec(Ser(concat(A,5*t-1))^(1/5))[n+1])==1,r=5*t-1, if(denominator(Vec(Ser(concat(A,5*t-2))^(1/5))[n+1])==1,r=5*t-2, if(denominator(Vec(Ser(concat(A,5*t-3))^(1/5))[n+1])==1,r=5*t-3,r=5*t-4)))));r}
{a(n)=local(B=[1]);if(n==0,1,for(k=1,n,t=3*a(k-1);B=concat(B,t); B[ #B]=t+1-denominator(Vec(Ser(B)^(1/2))[ #B]) ));B[n+1]}
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