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

0,3

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.

Links

Table of n, a(n) for n=0..50.

Formula

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

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}]

Crossrefs

Cf. A023434

Sequence in context: A258470 A248357 A047872 * A015851 A225529 A065156

Adjacent sequences: A173251 A173252 A173253 * A173255 A173256 A173257

Keyword

nonn

Author

Roger L. Bagula, Nov 22 2010

Status

approved