Re: pair sums applied to trignometry sums

*To*: mathgroup at smc.vnet.net*Subject*: [mg52530] Re: pair sums applied to trignometry sums*From*: Roger Bagula <tftn at earthlink.net>*Date*: Wed, 1 Dec 2004 05:57:48 -0500 (EST)*References*: <coefpd$rgi$1@smc.vnet.net>*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

This male/ female Fibonacci is another application of the pair type functions. In Mathematica: f[n_]:=(1/(n+1))^Mod[n,2]*(n/(n+1))^(1-Mod[n,2]) but g[n_]:=(n/(n+1))^Mod[n,2]*(1/(n+1))^(1-Mod[n,2]) doesn't seem to work. I had to change it to: g[n_]:=If[Mod[n,2]==1,(n/(n+1)),(1/(n+1))] The modulo power version seems functionallt equivalent, but fails completely in the zeta function versions of these. (* (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*)*) 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; ffib[n_Integer?Positive] :=ffib[n] =ffib[n-1]*f[n-1]+ffib[n-2]*f[n-2] ffib[0]=0;ffib[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; a=Table[Floor[ffib[n]*fib[n]],{n,0,digits}] b=Table[Floor[gfib[n]*fib[n]],{n,0,digits}] {0,1,0,1,1,3,4,7,11,18,29,47,75,123,197,321,514,836,1343,2181,3508,5692,9167, 14865,23959,38838,62635,101503,163773,265344,428291,693791,1120191,1814345, 2930173,4745365,7665395,12412755,20054413,32471888,52470417,84953526, 137291667,222271983,359249034,581585233,940082660,1521822386,2460102246, 3982297570,6438059697} {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, 3395454,5484273,8881231,14347563,23232342,37537787,60778546,98216903, 159015502,256996472,416059948,672493991,1088669150,1759816751,2848763556, 4605344794,7454779663}