

A151573


a(0)=1, a(1)=1; a(2^i + j) = a(j) + 2*a(j+1) for 0 <= j < 2^i.


16



1, 1, 3, 7, 3, 7, 17, 13, 3, 7, 17, 13, 17, 41, 43, 19, 3, 7, 17, 13, 17, 41, 43, 19, 17, 41, 43, 47, 99, 127, 81, 25, 3, 7, 17, 13, 17, 41, 43, 19, 17, 41, 43, 47, 99, 127, 81, 25, 17, 41, 43, 47, 99, 127, 81, 53, 99, 127, 137, 245, 353, 289, 131, 31, 3, 7, 17, 13, 17, 41, 43, 19, 17
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Equals A151572 + A151703.


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


MAPLE

N:= 10: # to get a(0) to a(2^(N+1)1)
a[0]:= 1:
a[1]:= 1:
for i from 1 to N do
for j from 0 to 2^i1 do
a[2^i+j]:= a[j]+2*a[j+1]
od
od:
seq(a[i], i=0..2^(N+1)1); # Robert Israel, May 28 2014


MATHEMATICA

a = {1, 1}; Do[AppendTo[a, a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jun 28 2017 *)


CROSSREFS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.
Sequence in context: A016665 A320831 A120124 * A113832 A115631 A053008
Adjacent sequences: A151570 A151571 A151572 * A151574 A151575 A151576


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 25 2009


STATUS

approved



