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A106222 Coefficients of g.f. A(x) where 0 <= a(n) <= 4 for all n>1, with initial terms {1,5}, such that A(x)^(1/5) consists entirely of integer coefficients.

%I A106222 #7 Mar 13 2015 19:18:15
%S A106222 1,5,0,0,0,1,0,0,0,0,3,0,0,0,0,1,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A106222 0,1,0,0,0,0,3,0,0,0,0,4,0,0,0,0,4,0,0,0,0,2,0,0,0,0,3,0,0,0,0,3,0,0,
%U A106222 0,0,3,0,0,0,0,4,0,0,0,0,1,0,0,0,0,3,0,0,0,0,1,0,0,0,0,1,0,0,0,0,4,0,0,0,0
%N A106222 Coefficients of g.f. A(x) where 0 <= a(n) <= 4 for all n>1, with initial terms {1,5}, such that A(x)^(1/5) consists entirely of integer coefficients.
%C A106222 Equals the self-convolution 5th power of A106223. What is the frequency of occurrence of the nonzero digits?
%F A106222 A(z)=0 at z=-0.1999361633111821182995648612577212067...
%e A106222 A(x) = 1 + 5*x + x^5 + 3*x^10 + x^15 + 4*x^20 + x^35 +...
%e A106222 A(x)^(1/5) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 +-...
%e A106222 A106223 = {1,1,-2,6,-21,80,-320,1326,-5637,24434,...}.
%o A106222 (PARI) {a(n)=local(A=1+5*x);if(n==0,1, for(j=1,n, for(k=0,4,t=polcoeff((A+k*x^j+x*O(x^j))^(1/5),j); if(denominator(t)==1,A=A+k*x^j;break))); return(polcoeff(A+x*O(x^n),n)))}
%Y A106222 Cf. A106223, A106216, A106220, A106224, A106226.
%K A106222 nonn
%O A106222 0,2
%A A106222 _Paul D. Hanna_, May 01 2005