login
A153010
Indices of A153007 where the entry equals zero.
0
0, 1, 2, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295
OFFSET
0,3
COMMENTS
It appears that this sequence is also the union of 2 and A000225. - Omar E. Pol, Mar 03 2011
LINKS
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.]
FORMULA
Conjectures from Colin Barker, Nov 24 2019: (Start)
G.f.: x*(1 - x - x^2 + 2*x^3) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>4.
a(n) = 2^(n-1) - 1 for n>2.
(End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 21 2008
EXTENSIONS
More terms a(7)-a(18) from Sean A. Irvine, Feb 22 2011
More terms a(19)-a(33) from Omar E. Pol, Mar 03 2011
STATUS
approved