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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.
5
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 01 2005
STATUS
approved