A158564 Generalized Fibonacci numbers round(abs(Fib(n*I))), I=sqrt(-1).

0, 5, 120, 2771, 64120, 1483771, 34335480, 794546793, 18386363119, 425473177569, 9845744025606, 227837336237557, 5272313768144476, 122004992372201577, 2823280028149695952, 65332655347676516331, 1511842896283885073147

Offset

0,2

Comments

Generalized Fib(x) = (phi^x - cos(x*Pi) / phi^x) / sqrt(5) where phi = (1 + sqrt(5))/2.

Links

Harry J. Smith, Table of n, a(n) for n = 0..100

Harry J. Smith, Generalized Fibonacci numbers

Example

a(2) = 120 because Fib(2*I) = -68.179... + 98.623... * I, whose absolute value is 119.895..., and rounded gives 120.

Prog

(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)) }

Crossrefs

Sequence in context: A307350 A322707 A160695 * A252928 A308363 A192639

Adjacent sequences: A158561 A158562 A158563 * A158565 A158566 A158567

Keyword

nonn

Author

Harry J. Smith, Mar 21 2009

Status

approved