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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.
9
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?
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 01 2005
STATUS
approved