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A048585 Pisot sequence L(6,7). 3
6, 7, 9, 12, 16, 22, 31, 44, 63, 91, 132, 192, 280, 409, 598, 875, 1281, 1876, 2748, 4026, 5899, 8644, 12667, 18563, 27204, 39868, 58428, 85629, 125494, 183919, 269545, 395036, 578952, 848494, 1243527, 1822476, 2670967, 3914491, 5736964, 8407928, 12322416, 18059377 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

FORMULA

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 50000 but is not known to hold in general).

MAPLE

L := proc(a0, a1, n)

    option remember;

    if n = 0 then

        a0 ;

    elif n = 1 then

        a1;

    else

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

    end if;

end proc:

A048585 := proc(n)

    L(6, 7, n) ;

end proc:

MATHEMATICA

RecurrenceTable[{a[0] == 6, a[1] == 7, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* Bruno Berselli, Feb 05 2016 *)

PROG

(MAGMA) Lxy:=[6, 7]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..50]]; // Bruno Berselli, Feb 05 2016

(PARI) first(n)=my(v=vector(n+1)); v[1]=6; v[2]=7; for(i=3, #v, v[i]=ceil(v[i-1]^2/v[i-2])); v \\ Charles R Greathouse IV, Feb 12 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A108595 A186079 A022938 * A169761 A049304 A168614

Adjacent sequences:  A048582 A048583 A048584 * A048586 A048587 A048588

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 22 13:09 EST 2018. Contains 299454 sequences. (Running on oeis4.)