A106220 Coefficients of g.f. A(x) where 0 <= a(n) <= 3 for all n>1, with initial terms {1,4}, such that A(x)^(1/4) consists entirely of integer coefficients.

1, 4, 2, 0, 3, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 3, 0, 2, 0, 3, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 3, 0, 2, 0, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 2, 0, 1, 0, 2, 0, 3, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1

Offset

0,2

Comments

Equals the self-convolution 4th power of A106221. What is the frequency of occurrence of the nonzero digits?

Links

Antti Karttunen, Table of n, a(n) for n = 0..1200

Formula

A(z)=0 at z=-0.30239090673234876830066191989552890839853849934485...

Example

A(x) = 1 + 4*x + 2*x^2 + 3*x^4 + 2*x^6 + x^8 + 2*x^14 +...
A(x)^(1/4) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 10*x^5 - 26*x^6 +-...
A106221 = {1,1,-1,2,-4,10,-26,71,-199,569,-1652,...}.

Prog

(PARI) {a(n)=local(A=1+4*x); if(n==0, 1, for(j=1, n, for(k=0, 3, t=polcoeff((A+k*x^j+x*O(x^j))^(1/4), j); if(denominator(t)==1, A=A+k*x^j; break))); return(polcoeff(A+x*O(x^n), n)))}

Crossrefs

Cf. A106221, A106216, A106222, A106224, A106226.

Sequence in context: A028956 A129681 A126079 * A176066 A309987 A350358

Adjacent sequences: A106217 A106218 A106219 * A106221 A106222 A106223

Keyword

nonn

Author

Paul D. Hanna, May 01 2005

Status

approved