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A117940
a(0)=1, thereafter a(3n) = a(3n+1)/3 = a(n), a(3n+2)=0.
21
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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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
OFFSET
0,2
COMMENTS
a(n) = a(3n)/a(0) = a(3n+1)/a(1). a(n) mod 2 = A039966(n). Row sums of A117939.
Observation: if this is written as a triangle (see example) then at least the first five row sums coincide with A002001. - Omar E. Pol, Nov 28 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
FORMULA
G.f.: Product_{k>=0} 1+3*x^(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
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.
Sequence in context: A010030 A372339 A197270 * A099093 A382025 A137339
KEYWORD
easy,nonn,tabf
AUTHOR
Paul Barry, Apr 05 2006
STATUS
approved