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A022032
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Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(5,26).
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11
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5, 26, 135, 700, 3629, 18813, 97527, 505582, 2620947, 13587040, 70435478, 365138879, 1892887004, 9812762803, 50869551972, 263708740319, 1367071205166, 7086923541985, 36738748574433, 190454382472052, 987319198674433, 5118281802804775, 26533271760636405, 137548993480193164
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OFFSET
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0,1
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COMMENTS
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The empirical g.f. / recurrence agrees with the original definition for at least 2000 terms (and a(2000) ~ 10^1430). - M. F. Hasler, Feb 11 2016
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LINKS
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FORMULA
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Empirical g.f.: -(x^6+x^5+x^4+x^3-x-5) / (x^7+x^6+x^5+x^4-x^2-5*x+1). - Colin Barker, Sep 18 2015
a(n+1) = ceiling(a(n)^2/a(n-1))-1 for all n > 0. - M. F. Hasler, Feb 11 2016
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MATHEMATICA
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(* This empirical recurrence should not be used to extend the data. *) LinearRecurrence[{5, 1, 0, -1, -1, -1, -1}, {5, 26, 135, 700, 3629, 18813, 97527}, 24] (* Jean-François Alcover, Dec 12 2016 *)
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PROG
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(PARI) a=[5, 26]; for(n=2, 2000, a=concat(a, ceil(a[n]^2/a[n-1])-1)); A022032(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016
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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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