A020706 Pisot sequences L(4,6), E(4,6).

4, 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

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = Fib(n+4)+1 = A000045(n+4)+1.

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

G.f.: (4-2*x-3*x^2)/(1-x)/(1-x-x^2). - Colin Barker, Feb 21 2012

Mathematica

CoefficientList[Series[(4-2*x-3*x^2)/(1-x)/(1-x-x^2), {x, 0, 40}], x](* Vincenzo Librandi, Apr 20 2012 *)

Prog

(Magma) I:=[4, 6, 9]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Apr 20 2012

Crossrefs

Subsequence of A001611, A048577. See A008776 for definitions of Pisot sequences.

Sequence in context: A118689 A364489 A118692 * A226271 A137371 A179463

Adjacent sequences: A020703 A020704 A020705 * A020707 A020708 A020709

Keyword

nonn,easy

Author

David W. Wilson

Status

approved