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A298590
Sum of terms of A293630 after generating the sequence for n steps (see comments).
2
3, 5, 9, 17, 47, 93, 185, 369, 1103, 2205, 4409, 13223, 26445, 52889, 105777, 317327, 634653, 1269305, 2538609, 5077217, 15231647, 30463293, 60926585, 182779751, 365559501, 731119001, 1462238001, 4386713999, 8773427997, 26320283987, 52640567973, 105281135945
OFFSET
0,1
COMMENTS
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.
A291481(n) < a(n) < 2*A291481(n).
Lim_{k->infinity} a(k)/A291481(k) = 1.275261... (see A296564).
Lim_{k->infinity} a(k)^(1/k) = 2.236151... (see A297890).
FORMULA
a(n) = Sum_{k=1..A291481(n)} A293630(k).
a(n) = (1 + A293630(A291481(n-1)))*a(n-1) - A293630(A291481(n-1))^2.
a(n) ~ d*A291481(n), where d = 1.275261... (see A296564).
a(n) = A298606(A291481(n)).
EXAMPLE
A293630 generated n times.
n = 0: [1, 2]; a(0) = 1 + 2 = 3.
n = 1: [1, 2, 1, 1]; a(1) = 1 + 2 + 1 + 1 = 5.
n = 2: [1, 2, 1, 1, 1, 2, 1]; a(2) = 1 + 2 + 1 + 1 + 1 + 2 + 1 = 9.
n = 3: [1, 2, 1, 1, 1, 2, ...]; a(2) = 1 + 2 + 1 + 1 + 1 + 2 + ... = 17.
...
PROG
(PARI) lista(nn) = {
my(S = [1, 2], t = 3, L, nPrev, E);
print1("3, ");
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, ", "));
E = S;
for(j = nn + 1, nn + #E, L = E[#E+1-(j-nn)]; t = t*(1+L)-L^2; print1(t, ", "));
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Iain Fox, Jan 22 2018
STATUS
approved