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A100582 Female of (1/(n+1),n/(1+n)) pair function used to get a dual population Fibonacci. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)