A298590 Sum of terms of A293630 after generating the sequence for n steps (see comments).

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).

Links

Iain Fox, Table of n, a(n) for n = 0..2860

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

Cf. A291481, A293630, A296564, A297890.

Sequence in context: A178717 A006723 A217097 * A262451 A096390 A092264

Adjacent sequences: A298587 A298588 A298589 * A298591 A298592 A298593

Keyword

nonn

Author

Iain Fox, Jan 22 2018

Status

approved