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 A117940 a(0)=1, thereafter a(3n) = a(3n+1)/3 = a(n), a(3n+2)=0. 19
 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 (list; graph; refs; listen; history; text; internal format)
 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. [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. Sequence in context: A139214 A010030 A197270 * A099093 A137339 A230184 Adjacent sequences:  A117937 A117938 A117939 * A117941 A117942 A117943 KEYWORD easy,nonn,tabf AUTHOR Paul Barry, Apr 05 2006 STATUS approved

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Last modified May 12 23:09 EDT 2021. Contains 343829 sequences. (Running on oeis4.)