%I A117940
%S A117940 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,
%T A117940 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,
%U A117940 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
%N A117940 a(0)=1,a(n)=a(3n)=a(3n+1)/3,a(3n+2)=0.
%C A117940 a(n)=a(3n)/a(0)=a(3n+1)/a(1). a(n) mod 2=A039966(n). Row sums of A117939.
%F A117940 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.
%Y A117940 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.
%Y A117940 Sequence in context: A154853 A139214 A010030 this_sequence A099093 A137339 
               A132330
%Y A117940 Adjacent sequences: A117937 A117938 A117939 this_sequence A117941 A117942 
               A117943
%K A117940 easy,nonn
%O A117940 0,2
%A A117940 Paul Barry (pbarry(AT)wit.ie), Apr 05 2006