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

0,1

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

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

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 *)

Prog

(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

Crossrefs

Cf. A022018 - A022025, A022026 - A022031.

Sequence in context: A047755 A047768 A375177 * A255118 A052918 A255633

Adjacent sequences: A022029 A022030 A022031 * A022033 A022034 A022035

Keyword

nonn

Author

R. K. Guy

Extensions

Edited by M. F. Hasler, Feb 11 2016

Status

approved