A157726 a(n) = Fibonacci(n) + 3.

3, 4, 4, 5, 6, 8, 11, 16, 24, 37, 58, 92, 147, 236, 380, 613, 990, 1600, 2587, 4184, 6768, 10949, 17714, 28660, 46371, 75028, 121396, 196421, 317814, 514232, 832043, 1346272, 2178312, 3524581, 5702890, 9227468, 14930355, 24157820, 39088172, 63245989, 102334158

Offset: 0

Author

N. J. A. Sloane, Jun 26 2010

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

Programs

Haskell

a157726 = (+ 3) . a000045
a157726_list = 3 : 4 : map (subtract 3)
                       (zipWith (+) a157726_list $ tail a157726_list)
-- Reinhard Zumkeller, Jul 30 2013

Magma

[ Fibonacci(n) + 3: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011

Mathematica

Fibonacci[Range[0,45]]+3 (* Harvey P. Dale, Oct 26 2011 *)

PARI

a(n)=fibonacci(n)+3 \\ Charles R Greathouse IV, Jul 02 2013

Formula

G.f.: ( 3-2*x-4*x^2 ) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Aug 08 2012

a(0) = 3, a(1) = 4, a(n) = a(n - 2) + a(n - 1) - 3. - Reinhard Zumkeller, Jul 30 2013