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A158510 Generalized Fibonacci numbers Fib(n + 0.5) rounded to an integer. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)