A151571 a(0)=1, a(1)=2; a(2^i + j) = a(j) + a(j+1) for 0 <= j < 2^i.

1, 2, 3, 5, 3, 5, 8, 8, 3, 5, 8, 8, 8, 13, 16, 11, 3, 5, 8, 8, 8, 13, 16, 11, 8, 13, 16, 16, 21, 29, 27, 14, 3, 5, 8, 8, 8, 13, 16, 11, 8, 13, 16, 16, 21, 29, 27, 14, 8, 13, 16, 16, 21, 29, 27, 19, 21, 29, 32, 37, 50, 56, 41, 17, 3, 5, 8, 8, 8, 13, 16, 11, 8, 13, 16, 16, 21, 29, 27, 14, 8, 13

Offset

0,2

Comments

Equals 2*A118977 + A151702.

Links

Ivan Neretin, Table of n, a(n) for n = 0..8191

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Mathematica

a = {1, 2}; Do[AppendTo[a, a[[j]] + 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: A122820 A261324 A224887 * A193957 A336746 A209769

Adjacent sequences: A151568 A151569 A151570 * A151572 A151573 A151574

Keyword

nonn

Author

N. J. A. Sloane, May 25 2009

Status

approved