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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

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,...}.

PROG

(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)))}

CROSSREFS

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

Sequence in context: A270032 A305671 A228633 * A229658 A306755 A005070

Adjacent sequences:  A106223 A106224 A106225 * A106227 A106228 A106229

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 01 2005

STATUS

approved

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Last modified October 20 19:57 EDT 2019. Contains 328269 sequences. (Running on oeis4.)