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.
Lim_{k->infinity} a(k)^(1/k) = 2.236151... (see A297890).
LINKS
Iain Fox, Table of n, a(n) for n = 0..2860
FORMULA
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