OFFSET
0,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..15625
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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
FORMULA
G.f.: Prod_{k >= 0 } (1+x^(5^k)). Exponents give A033042.
G.f. A(x) satisfies: A(x) = (1 + x) * A(x^5). - Ilya Gutkovskiy, Aug 12 2019
MATHEMATICA
m = 130; A[_] = 1;
Do[A[x_] = (1+x) A[x^5] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 19 2019 *)
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