OFFSET
0,2
COMMENTS
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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
FORMULA
G.f.: Product{k>=0, 1+3x^(3^k)}; a(n)=sum{k=0..n, sum{j=0..n, L(C(n,j)/3)*L(C(n-j,k)/3)}} where L(j/p) is the Legendre symbol of j and p.
EXAMPLE
Contribution from Omar E. Pol, Nov 26 2011 (Start):
When written as a triangle this begins:
1,
3,0,
3,9,0,0,0,0,
3,9,0,9,27,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,9,0,9,27,0,0,0,0,9,27,0,27,81,0,0,0,0,0,0,0,0,0,0,0,...
(End)
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
easy,nonn,tabf
AUTHOR
Paul Barry, Apr 05 2006
STATUS
approved