A173254 a(n) = a(n-1) + a(n-2) - [a(n-2)/2] - [a(n-4)/2].

1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 16, 19, 22, 26, 29, 33, 37, 41, 46, 51, 56, 62, 67, 73, 79, 85, 92, 99, 106, 114, 121, 129, 137, 145, 154, 163, 172, 182, 191, 201, 211, 221, 232, 243, 254, 266, 277, 289, 301, 313, 326

Offset: 0

Author

Roger L. Bagula, Nov 22 2010

Keywords

• nonn

Comments

The female population of Rabbits is; a(n)= f[n]-Floor[f[n]/2] Here that is the term: f[n - 2] - Floor[f[n - 2]/2] One natural child birth population limit is death by infection of the mothers. The fourth generation death of old age is the Floor[f[n - 4]/2] term. The resulting sequence approaches a stable population of rabbits at ratio one.

The ratio on the 300th iteration is approaching 1. Henry Bottomley did some of these half floor sequences, but not in the further generations.

Crossrefs

Cf. A023434

Programs

Mathematica

f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 2]/2] - Floor[f[n - 4]/2]
Table[f[n], {n, 0, 50}]

Formula

a(n)=a(n-1)+a(n-2)-Floor[a(n-2)/2]-Floor[a(n-4)/2]