OFFSET
0,4
COMMENTS
Generalized Fib(x) = (phi^x - cos(x*Pi) / phi^x) / sqrt(5) where phi = (1 + sqrt(5))/2.
Apparently, these are also the rounded geometric means of consecutive Fibonacci numbers. - Vladimir Reshetnikov, Mar 10 2021
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..500
Harry J. Smith, Generalized Fibonacci numbers
EXAMPLE
a(7) = 17 because Fib(7.5) = 16.51666... which rounds to 17.
MATHEMATICA
f[n_] := Round[(GoldenRatio^n - Cos[n*Pi]/GoldenRatio^n)/Sqrt[5]]; Array[f, 39, .5] (* Robert G. Wilson v, Jun 19 2014 *)
PROG
(PARI) { default(realprecision, 130); s5 = sqrt(5); phi = (1 + s5)/2.0; for (n=0, 500, x=n+0.5; f = round((phi^x - cos(x*Pi) / phi^x) / s5); write("b158510.txt", n, " ", f)) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Harry J. Smith, Mar 20 2009
STATUS
approved