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

Author

David W. Wilson

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Magma

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

PARI

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

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]