A022040 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(16,36).

16, 36, 80, 177, 391, 863, 1904, 4200, 9264, 20433, 45067, 99399, 219232, 483532, 1066464, 2352161, 5187855, 11442175, 25236512, 55660880, 122763936, 270764385, 597189651, 1317143239, 2905050864, 6407291380, 14131726000, 31168502865, 68744297111

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Comments

Not to be confused with the Pisot T(16,32) sequence, which is essentially A000079. - R. J. Mathar, Feb 13 2016

Apparently a(n) = A019489(n+2) = A077852(n+3) (Barker's recurrence) for n >= 0. - Georg Fischer, Mar 23 2019

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
• Index entries for Pisot sequences

Crossrefs

Cf. A019489, A077852.

Programs

PARI

T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a
T(16, 36, 30) \\ Colin Barker, Feb 16 2016

Formula

Empirical G.f.: (16-12*x+4*x^2-7*x^3)/(1-3*x+2*x^2-x^3+x^4). - Colin Barker, Feb 16 2012

a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016