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%I #18 Feb 16 2018 10:24:07
%S 3,5,9,17,47,93,185,369,1103,2205,4409,13223,26445,52889,105777,
%T 317327,634653,1269305,2538609,5077217,15231647,30463293,60926585,
%U 182779751,365559501,731119001,1462238001,4386713999,8773427997,26320283987,52640567973,105281135945
%N Sum of terms of A293630 after generating the sequence for n steps (see comments).
%C A293630, without generating it, starts as 1, 2. After 1 step, the block to the left is repeated twice and results in 1, 2, 1, 1. Generating a second step gives 1, 2, 1, 1, 1, 2, 1. This continues and a(n) is the sum of the terms at the n-th step.
%C A291481(n) < a(n) < 2*A291481(n).
%C Lim_{k->infinity} a(k)/A291481(k) = 1.275261... (see A296564).
%C Lim_{k->infinity} a(k)^(1/k) = 2.236151... (see A297890).
%H Iain Fox, <a href="/A298590/b298590.txt">Table of n, a(n) for n = 0..2860</a>
%F a(n) = Sum_{k=1..A291481(n)} A293630(k).
%F a(n) = (1 + A293630(A291481(n-1)))*a(n-1) - A293630(A291481(n-1))^2.
%F a(n) ~ d*A291481(n), where d = 1.275261... (see A296564).
%F a(n) = A298606(A291481(n)).
%e A293630 generated n times.
%e n = 0: [1, 2]; a(0) = 1 + 2 = 3.
%e n = 1: [1, 2, 1, 1]; a(1) = 1 + 2 + 1 + 1 = 5.
%e n = 2: [1, 2, 1, 1, 1, 2, 1]; a(2) = 1 + 2 + 1 + 1 + 1 + 2 + 1 = 9.
%e n = 3: [1, 2, 1, 1, 1, 2, ...]; a(2) = 1 + 2 + 1 + 1 + 1 + 2 + ... = 17.
%e ...
%o (PARI) lista(nn) = {
%o my(S = [1, 2], t = 3, L, nPrev, E);
%o print1("3, ");
%o for(j = 1, nn, L = S[#S]; t = t*(1+L)-L^2; nPrev = #S; for(r = 1, L, for(i = 1, nPrev-1, S = concat(S, S[i]))); print1(t, ", "));
%o E = S;
%o for(j = nn + 1, nn + #E, L = E[#E+1-(j-nn)]; t = t*(1+L)-L^2; print1(t, ", "));
%o }
%Y Cf. A291481, A293630, A296564, A297890.
%K nonn
%O 0,1
%A _Iain Fox_, Jan 22 2018
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