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A048577 Pisot sequence L(3,4). 5
3, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

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

a(n) = 1+[1/2+(1/2)*sqrt(5)]^n+(2/5)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(2/5)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+[1/2-(1/2)*sqrt(5)]^n, with n>0=0 - Paolo P. Lava, Jun 10 2008

a(n) = A020706(n-1), n>0. [From R. J. Mathar, Oct 15 2008]

G.f.: (3-2*x-2*x^2)/((1-x)*(1-x-x^2)). [Colin Barker, Apr 16 2012]

MATHEMATICA

CoefficientList[Series[(3-2*x-2*x^2)/((1-x)*(1-x-x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 27 2012 *)

PROG

(PARI) a(n)=fibonacci(n+3)+1 \\ Charles R Greathouse IV, Apr 16 2012

(MAGMA) [Fibonacci(n+3)+1: n in [0..40]]; // Vincenzo Librandi, Apr 27 2012

CROSSREFS

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

Sequence in context: A030712 A025000 A147790 * A107340 A291866 A173270

Adjacent sequences:  A048574 A048575 A048576 * A048578 A048579 A048580

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 17 17:12 EST 2019. Contains 320222 sequences. (Running on oeis4.)