cp's OEIS Frontend

A106224 Coefficients of g.f. A(x) where 0 <= a(n) <= 5 for all n>1, with initial terms {1,6}, such that A(x)^(1/6) consists entirely of integer coefficients.

%I A106224 #7 Mar 13 2015 00:04:30
%S A106224 1,6,3,2,3,0,0,0,3,4,3,0,0,0,3,2,0,0,0,0,3,2,0,0,4,0,0,2,0,0,2,0,0,0,
%T A106224 3,0,3,0,0,4,0,0,4,0,0,4,3,0,2,0,0,4,0,0,5,0,3,2,0,0,3,0,0,0,3,0,3,0,
%U A106224 3,0,3,0,2,0,3,0,0,0,2,0,0,0,3,0,2,0,0,0,3,0,5,0,3,0,0,0,3,0,0,0,0,0,4,0,0
%N A106224 Coefficients of g.f. A(x) where 0 <= a(n) <= 5 for all n>1, with initial terms {1,6}, such that A(x)^(1/6) consists entirely of integer coefficients.
%C A106224 Equals the self-convolution 6th power of A106225. What is the frequency of occurrence of the nonzero digits?
%F A106224 A(z)=0 at z=-0.18172379526003557530948965401615522817...
%e A106224 A(x) = 1 + 6*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^8 + 4*x^9 + 3*x^10 +...
%e A106224 A(x)^(1/6) = 1 + x - 2*x^2 + 7*x^3 - 27*x^4 + 114*x^5 - 506*x^6 +-...
%e A106224 A106225 = {1,1,-2,7,-27,114,-506,2322,-10919,52316,-254369,...}.
%o A106224 (PARI) {a(n)=local(A=1+6*x);if(n==0,1, for(j=1,n, for(k=0,5,t=polcoeff((A+k*x^j+x*O(x^j))^(1/6),j); if(denominator(t)==1,A=A+k*x^j;break))); return(polcoeff(A+x*O(x^n),n)))}
%Y A106224 Cf. A106225, A106216, A106220, A106222, A106226.
%K A106224 nonn
%O A106224 0,2
%A A106224 _Paul D. Hanna_, May 01 2005