A157729 a(n) = Fibonacci(n) + 5.

5, 6, 6, 7, 8, 10, 13, 18, 26, 39, 60, 94, 149, 238, 382, 615, 992, 1602, 2589, 4186, 6770, 10951, 17716, 28662, 46373, 75030, 121398, 196423, 317816, 514234, 832045, 1346274, 2178314, 3524583, 5702892, 9227470, 14930357, 24157822, 39088174, 63245991, 102334160

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

a157729 = (+ 5) . a000045
a157729_list = 5 : 6 : map (subtract 5)
                       (zipWith (+) a157729_list $ tail a157729_list)
-- Reinhard Zumkeller, Jul 30 2013

Magma

[ Fibonacci(n) + 5: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011

Mathematica

Fibonacci[Range[0,40]]+5 (* or *) LinearRecurrence[{2,0,-1},{5,6,6},50] (* Harvey P. Dale, Aug 17 2012 *)

PARI

a(n)=fibonacci(n)+5 \\ Charles R Greathouse IV, Jul 02 2013

Formula

G.f.: ( 5-4*x-6*x^2 ) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Aug 09 2012

a(0)=5, a(1)=6, a(2)=6, a(n)=2*a(n-1)+0*a(n-2)-a(n-3). - Harvey P. Dale, Aug 17 2012

a(0) = 5, a(1) = 6, a(n) = a(n - 2) + a(n - 1) - 5. - Reinhard Zumkeller, Jul 30 2013