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.

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, 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, 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

Offset: 0

Author

Paul D. Hanna, May 01 2005

Keywords

• nonn

Comments

Equals the self-convolution 7th power of A106227. What is the frequency of occurrence of the nonzero digits?

Examples

			A(x) = 1 + 7*x + x^7 + 4*x^14 + 6*x^21 + 5*x^28 + x^35 + 6*x^42 +...
A(x)^(1/7) = 1 + x - 3*x^2 + 13*x^3 - 65*x^4 + 351*x^5 - 1989*x^6 +-...
A106227 = {1,1,-3,13,-65,351,-1989,11650,-69900,427167,...}.
		

Crossrefs

Cf. A106227, A106216, A106220, A106222, A106224.

Programs

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)))}