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

Author

Paul Barry, Oct 11 2005

Keywords

• easy
• nonn

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.

Crossrefs

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

Programs

Mathematica

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

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

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

Extensions

More terms from Antti Karttunen, Aug 28 2017