0,2

Fixed point of the morphism a -> a, 2a, 3a, starting from a(1) = 1. - Robert G. Wilson v Jan 24 2006.

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.

Michael Gilleland, Some Self-Similar Integer Sequences

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

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

15 in base 3 is 120, here r=1 and s=1 so a(15) = 3*2 = 6.

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)

Nest[Flatten[ # /. a_Integer -> {a, 2a, 3a}] &, {1}, 4] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006)

(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)

Sequence in context: A140503 A043263 A118978 this_sequence A062068 A130542 A128502

Adjacent sequences: A006044 A006045 A006046 this_sequence A006048 A006049 A006050

nonn

Jeffrey Shallit

More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2003