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Male of (1/(n+1), n/(1+n)) pair function used to get a dual population Fibonacci.
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%I #8 Sep 07 2013 14:21:06

%S 0,1,0,1,1,3,4,7,11,18,29,47,75,123,197,321,514,836,1343,2181,3508,

%T 5692,9167,14865,23959,38838,62635,101503,163773,265344,428291,693791,

%U 1120191,1814345,2930173,4745365,7665395,12412755,20054413,32471888

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

%C 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 *)

%F 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]]

%K nonn,uned

%O 0,6

%A _Roger L. Bagula_, Nov 29 2004