%I A006047 M0422
%S A006047 1,2,3,2,4,6,3,6,9,2,4,6,4,8,12,6,12,18,3,6,9,6,12,18,9,18,27,2,4,6,4,
               8,
%T A006047 12,6,12,18,4,8,12,8,16,24,12,24,36,6,12,18,12,24,36,18,36,54,3,6,9,6,
%U A006047 12,18,9,18,27,6,12,18,12,24,36,18,36,54,9,18,27,18,36,54,27,54
%N A006047 Number of entries in n-th row of Pascal's triangle not divisible by 3.
%C A006047 Fixed point of the morphism a -> a, 2a, 3a, starting from a(1) = 1. - 
               Robert G. Wilson v Jan 24 2006.
%C A006047 This is a particular case of the number of entries in n-th row of Pascal's 
               triangle not divisible by a prime p, which is given by a simple recursion 
               using \otimes, the Kronecker (or tensor) product of vectors. Let 
               v_0=(1,2,...,p). Then v_{n+1)=v_0 \otimes v_n. The vector v_n contains 
               the values for the first p^n rows of Pascal's triangle (rows 0 through 
               p^n-1). - William B. Everett (bill(AT)chgnet.ru), Mar 29 2008
%D A006047 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006047 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical 
               Computer Sci., 98 (1992), 163-197.
%H A006047 J.-P. Allouche and J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/
               Papers/as0.ps">The ring of k-regular sequences</a>, Theoretical Computer 
               Sci., 98 (1992), 163-197.
%H A006047 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%F A006047 Write n in base 3; if the representation contains r 1's and s 2's then 
               a(n) = 3^s * 2^r. Also a(n) = Sum_{k=0, 1, .., n} (C(n, k)^2 mod 
               3). - Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
%F A006047 a(n) = b(n+1), with b(1)=1, b(2)=2, b(3n)=3b(n), b(3n+1)=b(n+1), b(3n+2)=2b(n+1). 
               - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2003
%e A006047 15 in base 3 is 120, here r=1 and s=1 so a(15) = 3*2 = 6.
%p A006047 p:=proc(n) local ct, k: ct:=0: for k from 0 to n do if binomial(n,k) 
               mod 3 = 0 then else ct:=ct+1 fi od: end: seq(p(n),n=0..82); (from 
               Emeric Deutsch)
%t A006047 Nest[Flatten[ # /. a_Integer -> {a, 2a, 3a}] &, {1}, 4] (from Robert 
               G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006)
%o A006047 (PARI) b(n)=if(n<3,n,if(n%3==0,3*b(n/3),if(n%3==1,1*b((n+2)/3),2*b((n+1)/
               3)))) (from Ralf Stephan)
%Y A006047 Sequence in context: A140503 A043263 A118978 this_sequence A062068 A130542 
               A128502
%Y A006047 Adjacent sequences: A006044 A006045 A006046 this_sequence A006048 A006049 
               A006050
%K A006047 nonn
%O A006047 0,2
%A A006047 Jeffrey Shallit
%E A006047 More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2003