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(1) = 5 counts (x,y) = (-1,0), (0,-1), (0,0), (0,1) and (1,0).
a(2) = 12 counts (x,y,z) = (-1,-1,0), (-1,0,-1), (-1,0,1), (-1,1,0), (0,-1,-1), (0,-1,1), (0,1,-1), (0,1,1), (1,-1,0), (1,0,-1), (1,0,1) and (1,1,0).
N:= 100: # to get a(0) to a(N) G:= (1+2*add(x^(j^3),j=1..floor(N^(1/3))))^3: S:= series(G,x,N+1): seq(coeff(S,x,j),j=0..N); # Robert Israel, Apr 08 2016
CoefficientList[(1 + 2 Sum[x^(j^3), {j, 4}])^3, x] (* Michael De Vlieger, Apr 08 2016 *)
a(n, k=3) = if(n==0, return(1)); if(k <= 0, return(0)); if(k == 1, return(ispower(n, 3))); my(count = 0); for(v = 0, sqrtnint(n, 3), count += (2 - (v == 0))*if(k > 2, a(n - v^3, k-1), if(ispower(n - v^3, 3), 2 - (n - v^3 == 0), 0))); count; \\ Daniel Suteu, Aug 15 2021
a(1) = 8 counts (x,y,z,u) = (-1,0,0,0), (0,-1,0,0), (0,0,-1,0), (0,0,0,-1) and 4 more tuples with -1 replaced by +1. a(2) = 24 counts (x,y,z,u) = (-1,-1,0,0), (-1,0,-1,0), (-1,0,0,-1), (-1,0,0,1) etc, all variants where two of the 4 values are zero and the other two +1 or -1.
a(n, k=4) = if(n==0, return(1)); if(k <= 0, return(0)); if(k == 1, return(ispower(n,3))); my(count = 0); for(v = 0, sqrtnint(n, 3), count += (2 - (v == 0))*if(k > 2, a(n - v^3, k-1), if(ispower(n - v^3, 3), 2 - (n - v^3 == 0), 0))); count; \\ Daniel Suteu, Aug 15 2021
m:=120; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*(&+[x^(j^4): j in [1..50]]))^2)); // G. C. Greubel, Oct 06 2018
seq(coeff(series((1+2*add(x^(j^4),j=1..n))^2,x,n+1), x, n), n = 0 .. 120); # Muniru A Asiru, Oct 07 2018
CoefficientList[Series[(1 + 2*Sum[x^(j^4), {j, 1, 100}])^2, {x, 0, 120}], x] (* G. C. Greubel, Oct 06 2018 *)
x='x+O('x^120); Vec((1+2*sum(j=1,50, x^(j^4)))^2) \\ G. C. Greubel, Oct 06 2018
a[n_]:=Length[Solve[x^3 + y^3 == n, {x, y}, Integers]]; Table[a[i], {i, 10000}]
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