A157727 a(n) = Fibonacci(n) + 4.

4, 5, 5, 6, 7, 9, 12, 17, 25, 38, 59, 93, 148, 237, 381, 614, 991, 1601, 2588, 4185, 6769, 10950, 17715, 28661, 46372, 75029, 121397, 196422, 317815, 514233, 832044, 1346273, 2178313, 3524582, 5702891, 9227469, 14930356, 24157821, 39088173, 63245990, 102334159

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

a157727 = (+ 4) . a000045
a157727_list = 4 : 5 : map (subtract 4)
                       (zipWith (+) a157727_list $ tail a157727_list)
-- Reinhard Zumkeller, Jul 30 2013

Magma

[ Fibonacci(n) + 4: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011

Mathematica

Fibonacci[Range[0,50]]+4 (* Harvey P. Dale, Jun 17 2011 *)

PARI

a(n)=fibonacci(n)+4 \\ Charles R Greathouse IV, Jul 02 2013

Formula

a(0) = 4, a(1) = 5, a(n) = a(n - 2) + a(n - 1) - 4. - Reinhard Zumkeller, Jul 30 2013

G.f.: (4 - 3*x - 5*x^2)/((1 - x)*(1 - x - x^2)). - Stefano Spezia, Jul 21 2024