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%I #13 Feb 24 2021 02:48:19
%S 0,1,3,11,3,11,39,31,3,11,39,31,39,139,171,71,3,11,39,31,39,139,171,
%T 71,39,139,171,179,495,791,555,151,3,11,39,31,39,139,171,71,39,139,
%U 171,179,495,791,555,151,39,139,171,179,495,791,555,259,495,791,879,1843,3363,3247
%N a(0) = 0, a(1) = 1; a(2^i + j) = 2a(j) + 3a(j + 1) for 0 <= j < 2^i.
%H Robert Israel, <a href="/A170856/b170856.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 f:= proc(n) option remember; local j;
%p j:= n - 2^ilog2(n);
%p 2*procname(j)+3*procname(j+1);
%p end proc:
%p f(0):= 0: f(1):= 1:
%p map(f, [$0..100]); # _Robert Israel_, Jun 12 2018
%t f[n_] := f[n] = With[{j = n - 2^Floor@Log[2, n]}, 2 f[j] + 3 f[j+1]];
%t f[0] = 0; f[1] = 1;
%t f /@ Range[0, 100] (* _Jean-François Alcover_, Aug 31 2020, after _Robert Israel_ *)
%K nonn,look
%O 0,3
%A _N. J. A. Sloane_, Jan 02 2010
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