A106216 Coefficients of g.f. A(x) where 0 <= a(n) <= 2 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients.

1, 3, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0

Offset

0,2

Comments

The self-convolution cube-root equals A106219. Positions of 1's is given by A106217. Positions of 2's is given by A106218. What is the frequency of occurrence of the 1's and 2's?

Links

Table of n, a(n) for n=0..104.

Formula

A(z)=0 at z=-0.322846893915891638743032676733152456643928599...

Example

A(x)^(1/3) = 1 + 1x - 1x^2 + 2x^3 - 4x^4 + 9x^5 - 21x^6 + 53x^6 -+...

Prog

(PARI) {a(n)=local(A=1+3*x); if(n==0, 1, if(n==1, 3, for(j=2, n, for(k=0, 2, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(A, n)))}

Crossrefs

Cf. A106217, A106218, A106219, A083953.

Sequence in context: A107093 A051830 A356098 * A035676 A369283 A129685

Adjacent sequences: A106213 A106214 A106215 * A106217 A106218 A106219

Keyword

nonn

Author

Paul D. Hanna, May 01 2005

Status

approved