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%I #8 Jan 31 2018 19:00:42
%S 1,1,1,2,1,2,3,5,1,2,3,5,6,8,11,16,1,2,3,5,6,8,11,16,17,19,22,27,33,
%T 41,52,68,1,2,3,5,6,8,11,16,17,19,22,27,33,41,52,68,69,71,74,79,85,93,
%U 104,120,137,156,178,205,238,279,331,399,1,2,3,5,6,8,11,16,17,19,22,27,33
%N Start with S(0)={1}, then S(k+1) equals the concatenation of S(k) with the partial sums of S(k); the limit gives this sequence.
%C The partial sums is A107947. Terms at positions 2^k forms A107948.
%H Ivan Neretin, <a href="/A107946/b107946.txt">Table of n, a(n) for n = 1..8192</a>
%e Concatenate the initial 2^3 terms: {1,1,1,2,1,2,3,5} to the partial sums {1,2,3,5,6,8,11,16}
%e to obtain the initial 2^4 terms: {1,1,1,2,1,2,3,5, 1,2,3,5,6,8,11,16}.
%t Nest[Join[#, Accumulate@#] &, {1}, 7] (* _Ivan Neretin_, Jan 31 2018 *)
%o (PARI) {a(n)=local(A=[1,1],B=[1]);for(i=1,#binary(n)-1, B=concat(B,vector(#B,k,polcoeff(Ser(A)/(1-x),#B+k-1)));A=concat(A,B););A[n]}
%Y Cf. A107947, A107948.
%K nonn,look
%O 1,4
%A _Paul D. Hanna_, May 28 2005
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