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.
Gabriel Stauth has authored 2 sequences.
Starting with A000027, the first term is 1 so we subtract 1 from the next 1 terms so the second term becomes 1. Now again we subtract 1 from the next 1 terms and the third term becomes 2. Subtract 2 from the next two terms of A000027 (4 and 5) to get 2 and 3. Subtract 2 from the next 2 terms (the 3 from 5 and 6) to get 1 and 4. The next term is 4 - 1 = 3. To carry on subtract 3 from the next 3 terms.
a212306 n = a212306_list !! (n-1)
a212306_list = f [1..] where
f (x:xs) = x : f ((map (subtract x) us) ++ vs)
where (us, vs) = splitAt x xs
-- Reinhard Zumkeller, Dec 16 2013
b:= proc(n) option remember; local l, t;
if n=1 then [1$2] else l:= b(n-1); t:= n-l[2];
zip((x, y)->x+y, [t$t+1], subsop(1=NULL, 2=0, l), 0) fi
end:
a:= n-> b(n)[1]:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 12 2013
b[n_] := b[n] = Module[{l, t, x, y, m}, If[n == 1, {1, 1}, l = b[n-1]; t = n-l[[2]]; x = Array[t&, t+1]; y = ReplacePart[l, {1 -> Sequence[], 2 -> 0}]; m = Max[Length[x], Length[y]]; Thread[PadRight[x, m] + PadRight[y, m]]]]; a[n_] := b[n] // First; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 27 2014, after Alois P. Heinz *)
{a(n)=local(A=vector(n+1,j,j)); for(k=1,n+1, A = Vec(Ser(A) - x^k*A[k]*(1-x^A[k])/(1-x) +x*O(x^n)));A[n]} \\ Paul D. Hanna, Nov 12 2013
for(n=1,100,print1(a(n),", "))
/* Vector returns 1000 terms: */
{A=vector(1000,j,j);for(k=1,#A, A = Vec(Ser(A) - x^k*A[k]*(1-x^A[k])/(1-x) +x*O(x^#A)));A} \\ Paul D. Hanna, Nov 12 2013
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