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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, 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

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 January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)