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{PARA 11 "" 1 "" {XPPMATH 20 "7QI$ChiG6\"I%bellGF$I)binomialGF$I)cartp
rodGF$I*characterGF$I'chooseGF$I,compositionGF$I)conjpartGF$I+decodepa
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0 62 "phi:=(1+sqrt(5))/2; phibar:=(1-sqrt(5))/2; evalf(phi/sqrt(5));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\"\"\"\"\"#F$*$\"\"&F#F#" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",&#\"\"\"\"\"#F$*$\"\"&F##!\"\"F%" }}{PARA 11 
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{MPLTEXT 1 0 233 "for n from 0 to 20 do\n    printf(\"n=%d, LowBnd=%f,
 f[%d]=%d, binet=%f, approx=%f, HighBnd=%f\\n\",\n          n,\n      \+
    evalf(35/50*phi^n),\n          n,fibonacci(n+1),\n          evalf(
1/sqrt(5)*(phi^(n+1) - phibar^(n+1))),\n          " }{MPLTEXT 1 0 25 "
evalf(phi/sqrt(5)*phi^n)," }{MPLTEXT 1 0 35 "\n          evalf(39/50*p
hi^n));\nod:" }}{PARA 6 "" 1 "" {TEXT 210 79 "n=0, LowBnd=0.700000, f[
0]=1, binet=1.000000, approx=0.723607, HighBnd=0.780000" }}{PARA 6 "" 
1 "" {TEXT 210 79 "n=1, LowBnd=1.132624, f[1]=1, binet=1.000000, appro
x=1.170820, HighBnd=1.262067" }{TEXT 210 80 "\nn=2, LowBnd=1.832624, f
[2]=2, binet=2.000000, approx=1.894427, HighBnd=2.042067" }{TEXT 210 
80 "\nn=3, LowBnd=2.965248, f[3]=3, binet=3.000000, approx=3.065248, H
ighBnd=3.304133" }{TEXT 210 80 "\nn=4, LowBnd=4.797871, f[4]=5, binet=
5.000000, approx=4.959675, HighBnd=5.346200" }{TEXT 210 80 "\nn=5, Low
Bnd=7.763119, f[5]=8, binet=8.000000, approx=8.024922, HighBnd=8.65033
3" }{TEXT 210 85 "\nn=6, LowBnd=12.560990, f[6]=13, binet=13.000000, a
pprox=12.984597, HighBnd=13.996532" }{TEXT 210 85 "\nn=7, LowBnd=20.32
4109, f[7]=21, binet=21.000000, approx=21.009519, HighBnd=22.646865" }
{TEXT 210 85 "\nn=8, LowBnd=32.885100, f[8]=34, binet=34.000000, appro
x=33.994116, HighBnd=36.643397" }{TEXT 210 85 "\nn=9, LowBnd=53.209209
, f[9]=55, binet=55.000000, approx=55.003636, HighBnd=59.290261" }
{TEXT 210 87 "\nn=10, LowBnd=86.094308, f[10]=89, binet=89.000000, app
rox=88.997752, HighBnd=95.933658" }{TEXT 210 92 "\nn=11, LowBnd=139.30
3517, f[11]=144, binet=143.999999, approx=144.001388, HighBnd=155.2239
19" }{TEXT 210 92 "\nn=12, LowBnd=225.397825, f[12]=233, binet=232.999
999, approx=232.999140, HighBnd=251.157576" }{TEXT 210 92 "\nn=13, Low
Bnd=364.701341, f[13]=377, binet=376.999997, approx=377.000528, HighBn
d=406.381495" }{TEXT 210 92 "\nn=14, LowBnd=590.099166, f[14]=610, bin
et=609.999996, approx=609.999668, HighBnd=657.539070" }{TEXT 210 93 "
\nn=15, LowBnd=954.800507, f[15]=987, binet=986.999993, approx=987.000195, HighBnd=1063.920565
" }{TEXT 210 97 "\nn=16, LowBnd=1544.899672, f[16]=1597, binet=1596.99
9987, approx=1596.999862, HighBnd=1721.459634" }{TEXT 210 97 "\nn=17, \+
LowBnd=2499.700176, f[17]=2584, binet=2583.999978, approx=2584.000056,
 HighBnd=2785.380197" }{TEXT 210 97 "\nn=18, LowBnd=4044.599845, f[18]
=4181, binet=4180.999962, approx=4180.999914, HighBnd=4506.839828" }
{TEXT 210 97 "\nn=19, LowBnd=6544.300018, f[19]=6765, binet=6764.99993
2, approx=6764.999964, HighBnd=7292.220020" }{TEXT 210 102 "\nn=20, Lo
wBnd=10588.899850, f[20]=10946, binet=10945.999890, approx=10945.99987
0, HighBnd=11799.059840" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "
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