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A018920 Pisot sequence T(3,10), a(n) = floor(a(n-1)^2/a(n-2)). 2
3, 10, 33, 108, 353, 1153, 3766, 12300, 40172, 131202, 428506, 1399501, 4570771, 14928140, 48755311, 159234864, 520061125, 1698519827, 5547366384, 18117700664, 59172417076, 193257136076, 631177877968, 2061427183105, 6732621943159, 21988745758766 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

FORMULA

a(n) = 3*a(n-1) + a(n-2) - a(n-4) - a(n-5) - a(n-6) (holds at least up to n = 1000 but is not known to hold in general).

MAPLE

PisotT := proc(a0, a1, n)

    option remember;

    if n = 0 then

        a0 ;

    elif n = 1 then

        a1;

    else

        floor( procname(a0, a1, n-1)^2/procname(a0, a1, n-2)) ;

    end if;

end proc:

A018920 := proc(n)

    PisotT(3, 10, n) ;

end proc: # R. J. Mathar, Feb 13 2016

MATHEMATICA

RecurrenceTable[{a[0] == 3, a[1] == 10, a[n] == Floor[a[n - 1]^2/a[n - 2] ]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 05 2016 *)

PROG

(MAGMA) Txy:=[3, 10]; [n le 2 select Txy[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 05 2016

(PARI) pisotT(nmax, a1, a2) = {

  a=vector(nmax); a[1]=a1; a[2]=a2;

  for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));

  a

}

pisotT(50, 3, 10) \\ Colin Barker, Jul 29 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A126184 A292397 A060557 * A271943 A255116 A006190

Adjacent sequences:  A018917 A018918 A018919 * A018921 A018922 A018923

KEYWORD

nonn

AUTHOR

R. K. Guy

EXTENSIONS

Corrected by David W. Wilson

STATUS

approved

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Last modified February 19 11:04 EST 2018. Contains 299330 sequences. (Running on oeis4.)