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A020712 Pisot sequences E(5,8), P(5,8). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A020687 A035423 A135455 * A182506 A111321 A020736

Adjacent sequences:  A020709 A020710 A020711 * A020713 A020714 A020715

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 22 12:46 EDT 2017. Contains 289669 sequences.