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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.

REFERENCES

Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.

LINKS

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

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

AUTHOR

Simon Plouffe

EXTENSIONS

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

STATUS

approved

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Last modified May 26 18:43 EDT 2017. Contains 287129 sequences.