A151708 a(0)=1, a(1)=2; a(2^i+j)=2*a(j)+2*a(j+1) for 0 <= j < 2^i.

1, 2, 6, 16, 6, 16, 44, 44, 6, 16, 44, 44, 44, 120, 176, 100, 6, 16, 44, 44, 44, 120, 176, 100, 44, 120, 176, 176, 328, 592, 552, 212, 6, 16, 44, 44, 44, 120, 176, 100, 44, 120, 176, 176, 328, 592, 552, 212, 44, 120, 176, 176, 328, 592, 552, 288, 328, 592, 704, 1008, 1840, 2288

Offset

0,2

Comments

Equals 2*A151705+A151706.

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

Maple

See A151702 for Maple code.

Mathematica

a = {1, 2}; Do[AppendTo[a, 2 a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 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: A009586 A009487 A009806 * A356370 A355096 A036046

Adjacent sequences: A151705 A151706 A151707 * A151709 A151710 A151711

Keyword

nonn

Author

N. J. A. Sloane, Jun 06 2009

Status

approved