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A010901 Pisot sequences E(4,7), P(4,7). 2
4, 7, 12, 21, 37, 65, 114, 200, 351, 616, 1081, 1897, 3329, 5842, 10252, 17991, 31572, 55405, 97229, 170625, 299426, 525456, 922111, 1618192, 2839729, 4983377, 8745217, 15346786, 26931732, 47261895, 82938844, 145547525, 255418101, 448227521, 786584466 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Essentially the same as A005251: a(n) = A005251(n+5).

See A008776 for definitions of Pisot sequences.

LINKS

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

S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016)

FORMULA

a(n) = 2a(n-1) - a(n-2) + a(n-3) for n>=3. (Proved using the PtoRv program of Ekhad-Sloane-Zeilberger.) - N. J. A. Sloane, Sep 09 2016

PROG

(PARI) pisotE(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]+1/2));

  a

}

pisotE(50, 4, 7) \\ Colin Barker, Jul 27 2016

CROSSREFS

Cf. A005251, A008776, A010925.

Sequence in context: A020732 A117949 A228879 * A187211 A023624 A123194

Adjacent sequences:  A010898 A010899 A010900 * A010902 A010903 A010904

KEYWORD

nonn,changed

AUTHOR

Simon Plouffe

EXTENSIONS

Edited by N. J. A. Sloane, Jul 26 2016

STATUS

approved

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Last modified July 25 10:39 EDT 2017. Contains 289792 sequences.