%I #20 Feb 24 2021 02:48:18

%S 0,1,2,3,7,15,31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535,

%T 131071,262143,524287,1048575,2097151,4194303,8388607,16777215,

%U 33554431,67108863,134217727,268435455,536870911,1073741823,2147483647,4294967295

%N Indices of A153007 where the entry equals zero.

%C It appears that this sequence is also the union of 2 and A000225. - _Omar E. Pol_, Mar 03 2011

%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>

%F Conjectures from _Colin Barker_, Nov 24 2019: (Start)

%F G.f.: x*(1 - x - x^2 + 2*x^3) / ((1 - x)*(1 - 2*x)).

%F a(n) = 3*a(n-1) - 2*a(n-2) for n>4.

%F a(n) = 2^(n-1) - 1 for n>2.

%F (End)

%Y Cf. A000217, A000225, A139250, A153006, A153007.

%K nonn

%O 0,3

%A _Omar E. Pol_, Dec 21 2008

%E More terms a(7)-a(18) from _Sean A. Irvine_, Feb 22 2011

%E More terms a(19)-a(33) from _Omar E. Pol_, Mar 03 2011