

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[n1]+fib[n2] fib[0]=0; fib[1] = 1; gfib[n_Integer?Positive] :=gfib[n] =gfib[n1]*g[n1]+gfib[n2]*g[n2] 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



