login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)