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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
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)