A157729 - OEIS

%I #23 Sep 08 2022 08:45:42

%S 5,6,6,7,8,10,13,18,26,39,60,94,149,238,382,615,992,1602,2589,4186,

%T 6770,10951,17716,28662,46373,75030,121398,196423,317816,514234,

%U 832045,1346274,2178314,3524583,5702892,9227470,14930357,24157822,39088174,63245991,102334160

%N a(n) = Fibonacci(n) + 5.

%H Vincenzo Librandi, <a href="/A157729/b157729.txt">Table of n, a(n) for n = 0..285</a>

%H Ivana Jovović and Branko Malešević, <a href="http://nntdm.net/volume-23-2017/number-1/28-38/">Some enumerations of non-trivial composition of the differential operations and the directional derivative</a>, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F G.f.: ( 5-4*x-6*x^2 ) / ( (x-1)*(x^2+x-1) ). - _R. J. Mathar_, Aug 09 2012

%F 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

%F a(0) = 5, a(1) = 6, a(n) = a(n - 2) + a(n - 1) - 5. - _Reinhard Zumkeller_, Jul 30 2013

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

%o (Magma) [ Fibonacci(n) + 5: n in [0..40] ]; // _Vincenzo Librandi_, Apr 24 2011

%o (PARI) a(n)=fibonacci(n)+5 \\ _Charles R Greathouse IV_, Jul 02 2013

%o (Haskell)

%o a157729 = (+ 5) . a000045

%o a157729_list = 5 : 6 : map (subtract 5)

%o                        (zipWith (+) a157729_list $ tail a157729_list)

%o -- _Reinhard Zumkeller_, Jul 30 2013

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

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Jun 26 2010