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

0, 1, 0, 1, 2, 3, 5, 8, 13, 20, 34, 54, 88, 141, 230, 368, 599, 962, 1562, 2512, 4077, 6562, 10644, 17149, 27804, 44827, 72655, 117201, 189907, 306473, 496500, 801528, 1298303, 2096510, 3395454, 5484273, 8881231, 14347563, 23232342, 37537787

Offset

0,5

Comments

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

Links

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

Formula

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

Mathematica

(* (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}]

Crossrefs

Sequence in context: A293644 A158415 A005347 * A193616 A273715 A093093

Adjacent sequences: A100579 A100580 A100581 * A100583 A100584 A100585

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 29 2004

Status

approved