A151706 - OEIS

A151706

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

1, 0, 2, 4, 2, 4, 12, 12, 2, 4, 12, 12, 12, 32, 48, 28, 2, 4, 12, 12, 12, 32, 48, 28, 12, 32, 48, 48, 88, 160, 152, 60, 2, 4, 12, 12, 12, 32, 48, 28, 12, 32, 48, 48, 88, 160, 152, 60, 12, 32, 48, 48, 88, 160, 152, 80, 88, 160, 192, 272, 496, 624, 424, 124, 2, 4, 12, 12, 12, 32, 48

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OFFSET

0,3

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, 0}; 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: A288416 A240893 A241108 * A055372 A241078 A198285

Adjacent sequences: A151703 A151704 A151705 * A151707 A151708 A151709

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2009

STATUS

approved