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..4 of the 3-convoluted tree are as follows; The path from the root is shown, with child nodes enclosed in []. GEN.0: [1]; GEN.1: 1->[3]; GEN.2: 1-3->[3,6,9]; GEN.3: 1-3-3->[1,4,7] 1-3-6->[1,4,7,10,13,16] 1-3-9->[1,4,7,10,13,16,19,22,25]; GEN.4: 1-3-3-1->[3] 1-3-3-4->[3,6,9,12] 1-3-3-7->[3,6,9,12,15,18,21] 1-3-6-1->[3] 1-3-6-4->[3,6,9,12] 1-3-6-7->[3,6,9,12,15,18,21] 1-3-6-10->[3,6,9,12,15,18,21,24,27,30] 1-3-6-13->[3,6,9,12,15,18,21,24,27,30,33,36,39] 1-3-6-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48] 1-3-9-1->[3] 1-3-9-4->[3,6,9,12] 1-3-9-7->[3,6,9,12,15,18,21] 1-3-9-10->[3,6,9,12,15,18,21,24,27,30] 1-3-9-13->[3,6,9,12,15,18,21,24,27,30,33,36,39] 1-3-9-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48] 1-3-9-19->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57] 1-3-9-22->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66 ] 1-3-9-25->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75]. Each path in the tree from the root node forms the initial terms of a self-convolution cube of a sequence of integer terms.
{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}
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