A020712 Pisot sequences E(5,8), P(5,8).

5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141

Offset

0,1

Comments

Pisano period lengths: 1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60,.. - R. J. Mathar, Aug 10 2012

Links

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

Tanya Khovanova, Recursive Sequences

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

Formula

a(n) = Fib(n+5). a(n) = a(n-1) + a(n-2).

O.g.f.: (5+3x)/(1-x-x^2). a(n)=A020701(n+1). - R. J. Mathar, May 28 2008

a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-11+5*sqrt(5))+(1+sqrt(5))^n*(11+5*sqrt(5))))/sqrt(5). - Colin Barker, Jun 05 2016

Mathematica

CoefficientList[Series[(-3 z - 5)/(z^2 + z - 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
LinearRecurrence[{1, 1}, {5, 8}, 40] (* Harvey P. Dale, Dec 28 2013 *)

Prog

(PARI) a(n)=fibonacci(n+5) \\ Charles R Greathouse IV, Jan 17 2012

Crossrefs

Subsequence of A020701 and hence A020695, A000045. See A008776 for definitions of Pisot sequences.

Trisections: A015448, A014445, A033887.

Sequence in context: A314463 A314464 A135455 * A369222 A369220 A364526

Adjacent sequences: A020709 A020710 A020711 * A020713 A020714 A020715

Keyword

nonn,easy

Author

David W. Wilson

Status

approved