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Search: id:A106224
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| A106224 |
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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. |
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+0
5
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equals the self-convolution 6-th power of A106225. What is the frequency of occurrence of the nonzero digits?
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FORMULA
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A(z)=0 at z=-0.18172379526003557530948965401615522817...
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EXAMPLE
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A(x) = 1 + 6*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^8 + 4*x^9 + 3*x^10 +...
A(x)^(1/6) = 1 + x - 2*x^2 + 7*x^3 - 27*x^4 + 114*x^5 - 506*x^6 +-...
A106225 = {1,1,-2,7,-27,114,-506,2322,-10919,52316,-254369,...}.
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PROGRAM
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(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)))}
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CROSSREFS
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Cf. A106225, A106216, A106220, A106222, A106226.
Sequence in context: A033326 A068996 A068924 this_sequence A129203 A083946 A153607
Adjacent sequences: A106221 A106222 A106223 this_sequence A106225 A106226 A106227
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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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