A019489 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(3,7).

3, 7, 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

a(n) = A077852(n+1) (Barker's recurrence) is correct at least up to n=32000. - R. J. Mathar, Feb 11 2016

Not to be confused with the Pisot T(3,7) sequence, which is A020746. - R. J. Mathar, Feb 13 2016

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.: -(x^3-x^2+2*x-3) / ((x-1)*(x^3+2*x-1)). [Colin Barker, Dec 21 2012]

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

Maple

A019489 := proc(n)
        option remember;
        if n <= 1 then
                op(n+1, [3, 7]) ;
        else
                a := procname(n-1)^2/procname(n-2) ;
                if type(a, 'integer') then
                        a-1 ;
                else
                        floor(a) ;
                fi;
        end if;
end proc: # R. J. Mathar, Feb 11 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(3, 7, 30) \\ Colin Barker, Feb 16 2016

Crossrefs

Sequence in context: A173514 A045891 A081037 * A077852 A218983 A020746

Adjacent sequences: A019486 A019487 A019488 * A019490 A019491 A019492

Keyword

nonn

Author

R. K. Guy

Status

approved