OFFSET
0,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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.]
Lukasz Merta, Composition inverses of the variations of the Baum-Sweet sequence, arXiv:1803.00292 [math.NT], 2018. See q(n) (with different offset) p. 9.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
FORMULA
G.f.: Prod_{k >= 0 } (1+x^(4^k)). Exponents give A000695.
G.f. A(x) satisfies: A(x) = (1 + x) * A(x^4). - Ilya Gutkovskiy, Aug 12 2019
MATHEMATICA
terms = 105;
kmax = Log[4, terms] // Ceiling;
CoefficientList[Product[1+x^(4^k), {k, 0, kmax}] + O[x]^(kmax terms), x][[1 ;; terms]] (* Jean-François Alcover, Jul 31 2018 *)
PROG
(Haskell)
a151666 n = fromEnum (n < 2 || m < 2 && a151666 n' == 1)
where (n', m) = divMod n 4
-- Reinhard Zumkeller, Dec 03 2011
CROSSREFS
For generating functions Prod_{k>=0} (1+a*x^(b^k)) for the following values of (a,b) see: (1,2) A000012 and A000027, (1,3) A039966 and A005836, (1,4) A151666 and A000695, (1,5) A151667 and A033042, (2,2) A001316, (2,3) A151668, (2,4) A151669, (2,5) A151670, (3,2) A048883, (3,3) A117940, (3,4) A151665, (3,5) A151671, (4,2) A102376, (4,3) A151672, (4,4) A151673, (4,5) A151674.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 30 2009
STATUS
approved