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A196344
Coefficients of g.f. A(x) where -2 <= a(n) <= 2 for all n>1, with initial terms {1,5}, such that A(x)^(1/5) consists entirely of integer coefficients.
3
1, 5, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,2
COMMENTS
A(z) = 0 at z = -0.1999360614 0060333411 6048445601 7524456163 6606200034 1004259693 ...
LINKS
EXAMPLE
G.f.: A(x) = 1 + 5*x + x^5 - 2*x^10 + x^15 - x^20 + x^35 - 2*x^40 - x^45 - 2*x^50 + x^55 + 2*x^65 - x^70 + 2*x^80 +...
where the following series consists entirely of integer coefficients:
A(x)^(1/5) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 + 1326*x^7 - 5637*x^8 + 24434*x^9 - 107542*x^10 +...+ A196345(n)*x^n +...
PROG
(PARI) {a(n)=local(A=1+5*x); if(n==0, 1, if(n%5==0, for(j=1, n, for(k=-2, 2, t=polcoeff((A+k*x^j+x*O(x^j))^(1/5), j);
if(denominator(t)==1, A=A+k*x^j; break)))); polcoeff(A+x*O(x^n), n))}
CROSSREFS
Cf. A196345 (5th root), A196346 (quintisection), A106222 (variant).
Sequence in context: A260911 A228631 A101194 * A106222 A368864 A368863
KEYWORD
sign
AUTHOR
Paul D. Hanna, Oct 01 2011
STATUS
approved