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%I #20 Feb 24 2021 02:48:18
%S 1,1,3,7,3,7,17,13,3,7,17,13,17,41,43,19,3,7,17,13,17,41,43,19,17,41,
%T 43,47,99,127,81,25,3,7,17,13,17,41,43,19,17,41,43,47,99,127,81,25,17,
%U 41,43,47,99,127,81,53,99,127,137,245,353,289,131,31,3,7,17,13,17,41,43,19,17
%N a(0)=1, a(1)=1; a(2^i + j) = a(j) + 2*a(j+1) for 0 <= j < 2^i.
%C Equals A151572 + A151703.
%H Robert Israel, <a href="/A151573/b151573.txt">Table of n, a(n) for n = 0..10000</a>
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%p N:= 10: # to get a(0) to a(2^(N+1)-1)
%p a[0]:= 1:
%p a[1]:= 1:
%p for i from 1 to N do
%p for j from 0 to 2^i-1 do
%p a[2^i+j]:= a[j]+2*a[j+1]
%p od
%p od:
%p seq(a[i],i=0..2^(N+1)-1); # _Robert Israel_, May 28 2014
%t a = {1, 1}; Do[AppendTo[a, a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* _Ivan Neretin_, Jun 28 2017 *)
%Y 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.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 25 2009
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