A173673 a(2k) = floor(F(k)/2), a(2k+1) = ceiling(F(k)/2), where F = A000045 is the Fibonacci sequence.

0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 10, 11, 17, 17, 27, 28, 44, 45, 72, 72, 116, 117, 188, 189, 305, 305, 493, 494, 798, 799, 1292, 1292, 2090, 2091, 3382, 3383, 5473, 5473, 8855, 8856, 14328, 14329, 23184, 23184, 37512, 37513, 60696, 60697, 98209, 98209, 158905, 158906, 257114, 257115, 416020, 416020

Offset

0,10

Comments

Original definition: Paired sequence: {male,female} ={Floor[A000045(n)/2],A000045[n]-Floor[A000045(n)/2]}

Shows excess of females over males in Fibonacci sequences.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Formula

a(2k) = floor(Fibonacci(k)/2), a(2k+1) = ceiling(Fibonacci(k)/2) = Fibonacci(k)-a(2k).

Empirical g.f.: x^3*(1+x+x^2+2*x^3+x^4+x^5) / ((1+x)*(1-x+x^2)*(1+x+x^2)*(1-x^2-x^4)). - Colin Barker, Aug 02 2016

Mathematica

Table[{Floor[Fibonacci[j]/
      2], Fibonacci[j] - Floor[Fibonacci[j]/2]}, {j, 0, 30}]
Flatten[%]

Prog

(PARI) a(n)=(fibonacci(n\2)+n%2)\2 \\ M. F. Hasler, Nov 24 2010

Crossrefs

Cf. A000045.

Sequence in context: A228117 A286218 A094997 * A330715 A018125 A292420

Adjacent sequences: A173670 A173671 A173672 * A173674 A173675 A173676

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Nov 24 2010

Status

approved