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A048625 Pisot sequence P(4,6). 3
4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925, 12322413, 18059374 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture: satisfies a linear recurrence having signature (1, 0, 1). - Harvey P. Dale, Jun 05 2021

LINKS

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

Index entries for Pisot sequences

FORMULA

a(n) = a(n-1) + a(n-3) (Checked up to n = 48000).

G.f.: (conjecture) (( Q(0)-1)/2 -(x+x^2+x^3+2*x^4+3*x^5))/x^6, where Q(k) = 1 + x^3 + (2*k+3)*x - x*(2*k+1 + x^2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013

MAPLE

P := 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)-1/2) ;

    end if;

end proc:

A048625 := proc(n)

    P(4, 6, n) ;

end proc: # R. J. Mathar, Feb 12 2016

PROG

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

  a=vector(nmax); a[1]=a1; a[2]=a2;

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

  a

}

pisotP(50, 4, 6) \\ Colin Barker, Aug 08 2016

CROSSREFS

Subsequence of A000930. See A008776 for definitions of Pisot sequences.

Sequence in context: A283623 A020747 A010737 * A120134 A241451 A288379

Adjacent sequences:  A048622 A048623 A048624 * A048626 A048627 A048628

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 23 09:39 EDT 2022. Contains 353975 sequences. (Running on oeis4.)