A173199 a(n) = a(n-1)+a(n-2)-Floor(a(n-3)/2)-Floor(a(n-8)/2); initial terms are 0, 1, 1, 2, 3, 5, 7, 11.

0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 35, 50, 72, 103, 147, 209, 297, 421, 597, 845, 1196, 1692, 2393, 3383, 4782, 6759, 9552, 13498, 19073, 26949, 38077, 53799, 76011, 107393, 151729, 214368, 302865, 427895, 604538, 854102

Offset: 0

Author

Roger L. Bagula, Nov 22 2010

Keywords

• nonn

Comments

A two wave dying rabbits type sequence with limiting ratio 1.41280984879641.

Crossrefs

Cf. A023438 (dying rabbits).

Programs

Magma

I:=[0, 1, 1, 2, 3, 5, 7, 11]; [ n le 8 select I[n] else Self(n-1)+Self(n-2)-(Self(n-3) div 2)-(Self(n-8) div 2): n in [1..40] ];

Mathematica

f[-6] = 0; f[-5] = 0; f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0;
f[0] = 0; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 3]/2] - Floor[f[n -8]/2];
Table[f[n], {n, 0, 30}]