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Search: id:A100582
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| A100582 |
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Female of (1/(n+1),n/(1+n)) pair function used to get a dual population Fibonacci. |
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1
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| 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
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OFFSET
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0,5
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COMMENT
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As far as I know this is new approach in Fibonacci populations. They paired are so the sum of both is the Fibonacci sequence.
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FORMULA
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a(n) = Floor[gfib[n]*fib[n]]
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MATHEMATICA
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* (1/(n+1), n/(1+n)) pair function used to get a dual population Fibonacci *) (* if the Fibonacci is a rabbit population, thn it has male and femal 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*) 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}]
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CROSSREFS
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Sequence in context: A092834 A080106 A005347 this_sequence A093093 A137290 A121104
Adjacent sequences: A100579 A100580 A100581 this_sequence A100583 A100584 A100585
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 29 2004
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