A157725 a(n) = Fibonacci(n) + 2.

2, 3, 3, 4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157

Offset

0,1

Comments

a(n) = A226649(2*n+1) - A226649(2*n). - Reinhard Zumkeller, Jul 30 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..285

K.-W. Chen, Greatest Common Divisors in Shifted Fibonacci Sequences, J. Int. Seq. 14 (2011) # 11.4.7

Ivana Jovović and Branko Malešević, Some enumerations of non-trivial composition of the differential operations and the directional derivative, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

G.f.: -(1+x)*(3*x-2) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Aug 08 2012

a(0) = 2, a(1) = 3, a(n) = a(n - 2) + a(n - 1) - 2. - Reinhard Zumkeller, Jul 30 2013

Mathematica

Fibonacci[Range[0, 50]] + 2 (* or *)
LinearRecurrence[{2, 0, -1}, {2, 3, 3}, 50] (* Paolo Xausa, Jul 28 2024 *)

Prog

(Magma) [ Fibonacci(n) + 2: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011
(PARI) a(n)=fibonacci(n)+2 \\ Charles R Greathouse IV, Jul 02 2013
(Haskell)
a157725 = (+ 2) . a000045
a157725_list = 2 : 3 : map (subtract 2)
                       (zipWith (+) a157725_list $ tail a157725_list)
-- Reinhard Zumkeller, Jul 30 2013

Crossrefs

Cf. A000045, A001611, A000071, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

Sequence in context: A065565 A309795 A017842 * A372592 A238394 A372595

Adjacent sequences: A157722 A157723 A157724 * A157726 A157727 A157728

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 26 2010

Status

approved