A169622 a(n) = a(n-1) + Fibonacci(n), a(1)=5.

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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..250

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

Formula

a(n) = 5 + A168193(n)/2.

a(n) = 2*a(n-1) - a(n-3) = 3 + A000045(n+2). - R. J. Mathar Dec 04 2009

G.f.: x*(-5+4*x+4*x^2) / ((1-x)*(x^2+x-1)). - R. J. Mathar Dec 04 2009

a(n) = 3 + (2^(-1-n)*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / sqrt(5). - Colin Barker, Apr 20 2017

Example

n=2: a(1)+Fibonacci(2) = 5+1 = 6.
n=3: a(2)+Fibonacci(3) = 6+2 = 8.

Mathematica

RecurrenceTable[{a[1]==5, a[n]==a[n-1]+Fibonacci[n]}, a[n], {n, 40}] (* or *) LinearRecurrence[{2, 0, -1}, {5, 6, 8}, 40] (* Harvey P. Dale, Jul 20 2011 *)

Prog

(Magma) [ n eq 1 select 5 else Self(n-1)+Fibonacci(n): n in [1..40] ];  // Klaus Brockhaus, Jan 31 2011
(PARI) Vec((5 - 4*x - 4*x^2) / ((1 - x)*(1 - x - x^2)) + O(x^40)) \\ Colin Barker, Apr 20 2017

Crossrefs

Cf. A166876, A168193, A000045.

Sequence in context: A022937 A030742 A048583 * A047321 A033158 A193569

Adjacent sequences: A169619 A169620 A169621 * A169623 A169624 A169625

Keyword

nonn,easy

Author

Geoff Ahiakwo, Dec 03 2009

Status

approved