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A020727 Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1). 5
2, 7, 24, 82, 280, 956, 3264, 11144, 38048, 129904, 443520, 1514272, 5170048, 17651648, 60266496, 205762688, 702517760, 2398545664, 8189147136, 27959497216, 95459694592, 325919783936, 1112759746560, 3799199418368, 12971278180352, 44286713884672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also Pisot sequence T(2,7). - R. K. Guy

It appears that a(n) = 4*a(n-1) - 2*a(n-2) (holds at least up to n = 1000 but is not known to hold in general).

The recurrence holds up to n = 10^5. - Ralf Stephan, Sep 03 2013

Empirical g.f.: (2-x)/(1-4*x+2*x^2). - Colin Barker, Feb 21 2012

LINKS

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

MATHEMATICA

RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 04 2016 *)

PROG

(MAGMA) Iv:=[2, 7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 04 2016

(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, 2, 7) \\ Colin Barker, Aug 08 2016

CROSSREFS

It appears that this is a subsequence of A003480.

See A008776 for definitions of Pisot sequences.

Sequence in context: A099463 A021000 A003480 * A088854 A000777 A144170

Adjacent sequences:  A020724 A020725 A020726 * A020728 A020729 A020730

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, Aug 17 2009 at the suggestion of R. J. Mathar.

STATUS

approved

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)