A100581 Male of (1/(n+1), n/(1+n)) pair function used to get a dual population Fibonacci.

0, 1, 0, 1, 1, 3, 4, 7, 11, 18, 29, 47, 75, 123, 197, 321, 514, 836, 1343, 2181, 3508, 5692, 9167, 14865, 23959, 38838, 62635, 101503, 163773, 265344, 428291, 693791, 1120191, 1814345, 2930173, 4745365, 7665395, 12412755, 20054413, 32471888

Offset

0,6

Comments

These are rational functions and to get an integer popoulation a Floor[] function is necessary.(* if the Fibonacci is a rabbit population, then it has male and female components *) (* in this case the gfib (female) population is always larger or the same *) (* natural birth rate has the female popoulation slightly larger than the male in many mammals *) (* ratios of both populations still approach the golden mean *)

Links

Table of n, a(n) for n=0..39.

Formula

f[n_]:=(1/(n+1))^mod[n, 2]*(n/(n+1))^(1-mod[n, 2]) fib[n_Integer?Positive] :=fib[n] =fib[n-1]+fib[n-2] fib[0]=0;fib[1] = 1; ffib[n_Integer?Positive] :=ffib[n] =ffib[n-1]*f[n-1]+ffib[n-2]*f[n-2] ffib[0]=0;ffib[1] = 1; a(n) = Floor[ffib[n]*fib[n]]

Crossrefs

Sequence in context: A319106 A250296 A279785 * A093090 A193686 A000204

Adjacent sequences: A100578 A100579 A100580 * A100582 A100583 A100584

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 29 2004

Status

approved