A158510 Generalized Fibonacci numbers Fib(n + 0.5) rounded to an integer.

1, 1, 1, 2, 4, 6, 10, 17, 27, 43, 70, 113, 183, 296, 480, 776, 1255, 2031, 3287, 5318, 8605, 13924, 22529, 36452, 58981, 95433, 154414, 249848, 404262, 654109, 1058371, 1712481, 2770852, 4483332, 7254184, 11737517, 18991701, 30729218, 49720919

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

Cf. A001622.

Sequence in context: A091611 A107742 A228779 * A004695 A014216 A192683

Adjacent sequences: A158507 A158508 A158509 * A158511 A158512 A158513

Keyword

nonn

Author

Harry J. Smith, Mar 20 2009

Status

approved