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A301650
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Number of longest cycles in the n-Apollonian network.
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2
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OFFSET
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1,1
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COMMENTS
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a(8) has 106 decimal digits and a(9) has 213 decimal digits.
The circumference or length of the longest cycle is given by 7*2^(n-2) for n > 1. For n = 1, the circumference is 4. (End)
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LINKS
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PROG
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(PARI)
P(c, d, x)={[d^2 + 6*c*d + 2*d^3 + 2*x*(c + 3*d^2) + 2*x^2*d, c + d + 3*d^2 + 4*x*d + x^2]}
R(c, d, x)={4*d^3 + 9*c*d^2 + 3*d^2 + 6*c*d + 3*c^2 + 6*x*(2*d^3 + 3*d^2 + 4*c*d) + 3*x^2*(10*d^2 + 3*d + 3*c) + x^3*(18*d + 1) + 3*x^4}
a(n)={my(s=x^3, c=0, d=0); for(i=1, n, s = 3*s + R(c, d, x); [c, d]=P(c, d, x)); pollead(s)} \\ Andrew Howroyd, Sep 10 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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