A014306 a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.

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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). - Reinhard Zumkeller, Oct 14 2008

Characteristic function of A145397.

Examples

			From _David A. Corneth_, Oct 01 2018: (Start)
For n = 0, floor((6*0-1) ^ (1/3)) = -1. binomial(-1 + 2, 3) = n so a(0) = 0.
For n = 10, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) = n so a(10) = 0.
For n = 11, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) != n so a(11) = 1. (End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for characteristic functions

Crossrefs

Cf. A000292, A023533, A145397.

Programs

PARI

A014306(n) = { my(k=0); while(binomial(k+2,3)Antti Karttunen, Sep 30 2018

PARI

a(n) = if(n==0, return(0)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) != n \\ David A. Corneth, Oct 01 2018

PARI

first(n) = my(res = vector(n+1, i, 1), ov = nv = [1,2,1,0]); while(nv[4]<=n, res[nv[4]+1] = 0; for(i = 2, 4, nv[i] = ov[i-1] + ov[i]); ov = nv); res \\ David A. Corneth, Oct 01 2018

Extensions

Data section extended up to a(120) by Antti Karttunen, Sep 30 2018