A018915 Define the generalized Pisot 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). This is T(2,6).

2, 6, 17, 48, 135, 379, 1064, 2987, 8385, 23538, 66074, 185477, 520654, 1461532, 4102678, 11516659, 32328502, 90749586, 254743859, 715093440, 2007344278, 5634831512, 15817578736, 44401646533, 124640202381, 349878467638, 982146528794, 2756991050447

Offset

0,1

Comments

Not to be confused with the Pisot T(2,6) sequence, which is A008776. - 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

Maple

A018915 := proc(n)
    option remember;
    if n <= 1 then
        op(n+1, [2, 6]) ;
    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 10 2016

Mathematica

RecurrenceTable[{a[1] == 2, a[2] == 6, a[n] == Ceiling[a[n - 1]^2/a[n - 2]] - 1}, a, {n, 30}] (* Bruno Berselli, Feb 17 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(2, 6, 30) \\ Colin Barker, Feb 14 2016
(Magma) Tiv:=[2, 6]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..40]]; // Bruno Berselli, Feb 17 2016

Crossrefs

Sequence in context: A090039 A299166 A136776 * A019487 A077936 A077983

Adjacent sequences: A018912 A018913 A018914 * A018916 A018917 A018918

Keyword

nonn

Author

R. K. Guy

Status

approved