A147997 Number of nonnegative even integers <= Fibonacci(n).

1, 1, 1, 2, 2, 3, 5, 7, 11, 18, 28, 45, 73, 117, 189, 306, 494, 799, 1293, 2091, 3383, 5474, 8856, 14329, 23185, 37513, 60697, 98210, 158906, 257115, 416021, 673135, 1089155, 1762290, 2851444, 4613733, 7465177, 12078909

Offset: 0

Author

Giovanni Teofilatto, Nov 19 2008

Keywords

• easy
• nonn

Crossrefs

Cf. A000045

Programs

Mathematica

Table[f=Fibonacci[n]; If[EvenQ[f], f = f/2, f = (f-1)/2];  f+1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Nov 22 2010 *)

Formula

a(n) = 1+floor( A000045(n)/2) = 1+A004695(n). - R. J. Mathar, Jan 30 2010

From Chai Wah Wu, Sep 23 2016: (Start)

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5) for n > 4.

G.f.: (1 + x)*(1 - x - x^3)/((1 - x)*(1 - x - x^2)*(1 + x + x^2)). (End)

Extensions

Definition and offset corrected by R. J. Mathar, Jan 30 2010

Definition corrected by Joel B. Lewis, Nov 14 2012