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

0,4

Links

Table of n, a(n) for n=0..37.

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)

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 *)

Crossrefs

Cf. A000045

Sequence in context: A226498 A196375 A300440 * A218557 A060699 A118987

Adjacent sequences: A147994 A147995 A147996 * A147998 A147999 A148000

Keyword

easy,nonn

Author

Giovanni Teofilatto, Nov 19 2008

Extensions

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

Definition corrected by Joel B. Lewis, Nov 14 2012

Status

approved