A022032 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).

5, 26, 135, 700, 3629, 18813, 97527, 505582, 2620947, 13587040, 70435478, 365138879, 1892887004, 9812762803, 50869551972, 263708740319, 1367071205166, 7086923541985, 36738748574433, 190454382472052, 987319198674433, 5118281802804775, 26533271760636405, 137548993480193164

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Comments

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A022018 - A022025, A022026 - A022031.

Programs

Mathematica

(* 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 *)

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

Formula

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

Extensions

Edited by M. F. Hasler, Feb 11 2016