A113047 a(n) = C(3n,n)/(2n+1) mod 3.

1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 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, 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, 1

Offset

0,1

Comments

a(n) differs from 0 only when n=(3^j-1)/2, j>=0. [Conjecture confirmed by Kevin Ryde, Jun 23 2021; see links]

Characteristic function of the ternary repunits, a(n) = 1 iff n is a ternary repunit (A003462). - Kevin Ryde, Jun 23 2021

Links

Antti Karttunen, Table of n, a(n) for n = 0..29524

Kevin Ryde, Proof of characteristic function of the ternary repunits.

Formula

G.f.: A(x) satisfies A(x)=1+x*A(x^3). - Vladimir Kruchinin, Mar 24 2015

a(n) = A001764(n) mod 3. - Michel Marcus, Mar 24 2015

a(n) = floor(log_3(2*n + 1)) - floor(log_3(2*n - 1)), for n>=1. - Ridouane Oudra, Aug 24 2021

Mathematica

Table[Mod[Binomial[3 n, n]/(2 n + 1), 3], {n, 0, 72}] (* Michael De Vlieger, Mar 24 2015 *)

Prog

(PARI) A113047(n) = ((binomial(3*n, n)/(n+n+1))%3); \\ Antti Karttunen, Aug 28 2017
(PARI) a(n) = while(n, my(r); [n, r]=divrem(n, 3); if(r!=1, return(0))); 1; \\ Kevin Ryde, Jun 23 2021

Crossrefs

Cf. A001764, A003462 (indices of 1's), A010872, A039969.

Sequence in context: A015024 A016039 A138149 * A214505 A127692 A014305

Adjacent sequences: A113044 A113045 A113046 * A113048 A113049 A113050

Keyword

easy,nonn

Author

Paul Barry, Oct 11 2005

Extensions

More terms from Antti Karttunen, Aug 28 2017

Status

approved