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A151702 a(0)=1, a(1)=0; a(2^i + j) = a(j) + a(j+1) for 0 <= j < 2^i. 17
1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 3, 4, 3, 1, 1, 2, 2, 2, 3, 4, 3, 2, 3, 4, 4, 5, 7, 7, 4, 1, 1, 2, 2, 2, 3, 4, 3, 2, 3, 4, 4, 5, 7, 7, 4, 2, 3, 4, 4, 5, 7, 7, 5, 5, 7, 8, 9, 12, 14, 11, 5, 1, 1, 2, 2, 2, 3, 4, 3, 2, 3, 4, 4, 5, 7, 7, 4, 2, 3, 4, 4, 5, 7, 7, 5, 5, 7, 8, 9, 12, 14, 11, 5, 2, 3, 4, 4, 5, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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

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

MAPLE

f:=proc(r, s, a, b) local s1, n, i, j;

s1:=array(0..120);

s1[0]:=r; s1[1]:=s;

for n from 2 to 120 do i:=floor(log(n)/log(2));

j:=n-2^i; s1[n]:=a*s1[j]+b*s1[j+1]; od:

[seq(s1[n], n=0..120)];

end;

f(1, 0, 1, 1);

MATHEMATICA

a = {1, 0}; 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.

If first two terms are dropped, same as A151552.

Sequence in context: A000174 A156268 A053257 * A151552 A160418 A168115

Adjacent sequences:  A151699 A151700 A151701 * A151703 A151704 A151705

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2009

STATUS

approved

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)