A048577 Pisot sequence L(3,4).

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

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) = 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 A326655 A291866

Adjacent sequences: A048574 A048575 A048576 * A048578 A048579 A048580

Keyword

nonn,easy

Author

David W. Wilson

Status

approved