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

0,1

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

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

Prog

(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

Crossrefs

Cf. A019489, A077852.

Sequence in context: A295016 A125240 A050775 * A074985 A229134 A378794

Adjacent sequences: A022037 A022038 A022039 * A022041 A022042 A022043

Keyword

nonn

Author

R. K. Guy

Status

approved