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Search: id:A106216
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| A106216 |
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Coefficients of g.f. A(x) where 0 <= a(n) <= 2 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients. |
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+0
9
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| 1, 3, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The self-convolution cube-root equals A106219. Positions of 1's is given by A106217. Positions of 2's is given by A106218. What is the frequency of occurrence of the 1's and 2's?
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FORMULA
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A(z)=0 at z=-0.322846893915891638743032676733152456643928599...
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EXAMPLE
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A(x)^(1/3) = 1 + 1x - 1x^2 + 2x^3 - 4x^4 + 9x^5 - 21x^6 + 53x^6 -+...
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PROGRAM
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(PARI) {a(n)=local(A=1+3*x); if(n==0, 1, if(n==1, 3, for(j=2, n, for(k=0, 2, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(A, n)))}
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CROSSREFS
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Cf. A106217, A106218, A106219, A083953.
Sequence in context: A098018 A107093 A051830 this_sequence A035676 A129685 A091959
Adjacent sequences: A106213 A106214 A106215 this_sequence A106217 A106218 A106219
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2005
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