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A106226 Coefficients of g.f. A(x) where 0 <= a(n) <= 6 for all n>1, with initial terms {1,7}, such that A(x)^(1/7) consists entirely of integer coefficients.

%I A106226 #7 Mar 12 2015 22:55:03
%S A106226 1,7,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,6,0,0,0,0,0,0,5,0,0,0,0,0,
%T A106226 0,1,0,0,0,0,0,0,6,0,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,6,0,0,0,0,
%U A106226 0,0,5,0,0,0,0,0,0,1,0,0,0,0,0,0,5,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A106226 Coefficients of g.f. A(x) where 0 <= a(n) <= 6 for all n>1, with initial terms {1,7}, such that A(x)^(1/7) consists entirely of integer coefficients.
%C A106226 Equals the self-convolution 7th power of A106227. What is the frequency of occurrence of the nonzero digits?
%e A106226 A(x) = 1 + 7*x + x^7 + 4*x^14 + 6*x^21 + 5*x^28 + x^35 + 6*x^42 +...
%e A106226 A(x)^(1/7) = 1 + x - 3*x^2 + 13*x^3 - 65*x^4 + 351*x^5 - 1989*x^6 +-...
%e A106226 A106227 = {1,1,-3,13,-65,351,-1989,11650,-69900,427167,...}.
%o A106226 (PARI) {a(n)=local(A=1+7*x);if(n==0,1, for(j=1,n, for(k=0,6,t=polcoeff((A+k*x^j+x*O(x^j))^(1/7),j); if(denominator(t)==1,A=A+k*x^j;break))); return(polcoeff(A+x*O(x^n),n)))}
%Y A106226 Cf. A106227, A106216, A106220, A106222, A106224.
%K A106226 nonn
%O A106226 0,2
%A A106226 _Paul D. Hanna_, May 01 2005