|
%I #19 Apr 23 2020 04:23:20
%S 0,5,120,2771,64120,1483771,34335480,794546793,18386363119,
%T 425473177569,9845744025606,227837336237557,5272313768144476,
%U 122004992372201577,2823280028149695952,65332655347676516331,1511842896283885073147
%N Generalized Fibonacci numbers round(abs(Fib(n*I))), I=sqrt(-1).
%C Generalized Fib(x) = (phi^x - cos(x*Pi) / phi^x) / sqrt(5) where phi = (1 + sqrt(5))/2.
%H Harry J. Smith, <a href="/A158564/b158564.txt">Table of n, a(n) for n = 0..100</a>
%H Harry J. Smith, <a href="https://www.oocities.org/hjsmithh/Fibonacc/FibWhat.html">Generalized Fibonacci numbers</a>
%e a(2) = 120 because Fib(2*I) = -68.179... + 98.623... * I, whose absolute value is 119.895..., and rounded gives 120.
%o (PARI) { default(realprecision, 150); s5 = sqrt(5); phi = (1 + s5)/2.0; for (n=0, 100, x=n*I; f = round(abs((phi^x - cos(x*Pi) / phi^x) / s5)); write("b158564.txt",n," ",f)) }
%K nonn
%O 0,2
%A _Harry J. Smith_, Mar 21 2009
|
