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A020717 Pisot sequences L(6,9), E(6,9). 3
6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, 5702888, 9227466, 14930353, 24157818, 39088170, 63245987, 102334156, 165580142 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Index entries for Pisot sequences

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

FORMULA

a(n) = Fibonacci(n+5)+1 = A001611(n+5).

a(n) = 2*a(n-1) - a(n-3).

a(n) = 1 + (5/2)*(1/2 + (1/2)*sqrt(5))^n + (11/10)*(1/2 +(1/2)*sqrt(5))^n*sqrt(5) - (11/10)*sqrt(5)*(1/2 - (1/2)*sqrt(5))^n + (5/2)*(1/2 - (1/2)*sqrt(5))^n. - Paolo P. Lava, Jun 10 2008

a(n) = A020706(n+1). - R. J. Mathar, Oct 25 2008

MATHEMATICA

Table[Fibonacci[n + 5] + 1, {n, 0, 36}] (* Michael De Vlieger, Jul 27 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, 6, 9) \\ Colin Barker, Jul 27 2016

CROSSREFS

Subsequence of A001611, A048577.

See A008776 for definitions of Pisot sequences.

Pairwise sums of A018910.

Sequence in context: A316019 A316020 A300573 * A196993 A303162 A242042

Adjacent sequences:  A020714 A020715 A020716 * A020718 A020719 A020720

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 19 11:31 EDT 2018. Contains 316359 sequences. (Running on oeis4.)