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A100582 Female of (1/(n+1),n/(1+n)) pair function used to get a dual population Fibonacci. 0

%I

%S 0,1,0,1,2,3,5,8,13,20,34,54,88,141,230,368,599,962,1562,2512,4077,

%T 6562,10644,17149,27804,44827,72655,117201,189907,306473,496500,

%U 801528,1298303,2096510,3395454,5484273,8881231,14347563,23232342,37537787

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

%C As far as I know this is new approach in Fibonacci populations. They are paired so the sum of both is the Fibonacci sequence.

%F a(n) = Floor[gfib[n]*fib[n]]

%t (* (1/(n+1), n/(1+n)) pair function used to get a dual population Fibonacci *) (* 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 that of the male in many mammals *) (* ratios of both populations still approach the golden mean *) digits=50 f[n_]:=(1/(n+1))^ Mod[n, 2]*(n/(n+1))^(1- Mod[n, 2]) g[n_]:=If[ Mod[n, 2]==1, (n/(n+1)), (1/(n+1))] fib[n_Integer?Positive] :=fib[n] =fib[n-1]+fib[n-2] fib[0]=0;fib[1] = 1; gfib[n_Integer?Positive] :=gfib[n] =gfib[n-1]*g[n-1]+gfib[n-2]*g[n-2] gfib[0]=0;gfib[1] = 1; b=Table[Floor[gfib[n]*fib[n]], {n, 0, digits}]

%K nonn,uned

%O 0,5

%A _Roger L. Bagula_, Nov 29 2004

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Last modified May 23 02:17 EDT 2022. Contains 353959 sequences. (Running on oeis4.)