A127217 Half-indexed Fibonacci numbers a(n)=round(sqrt((1+sqrt(5))/2)^n/sqrt(5)) a(2n)=F(n)=A000045, so a(n)=F(n/2).

1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 17, 21, 27, 34, 43, 55, 70, 89, 113, 144, 183, 233, 296, 377, 480, 610, 776, 987, 1255, 1597, 2031, 2584, 3287, 4181, 5318, 6765, 8605, 10946, 13924, 17711, 22529, 28657, 36452, 46368

Offset

1,6

Comments

a(n)+a(n+2)=a(n+4), a(n+4)+1 or a(n+4)-1.

Links

Table of n, a(n) for n=1..48.

Maple

for n from 1 to 60 do a[n]:=round(sqrt((1+sqrt(5))/2)^n/sqrt(5)) od: seq(a[n], n=1..60);

Mathematica

Table[Round[(Sqrt[GoldenRatio])^n/Sqrt[5]], {n, 50}] (* Harvey P. Dale, Aug 22 2019 *)

Crossrefs

Cf. A000045.

Sequence in context: A266751 A063827 A241651 * A240735 A057042 A063595

Adjacent sequences: A127214 A127215 A127216 * A127218 A127219 A127220

Keyword

easy,nonn

Author

Miklos Kristof, Mar 28 2007

Status

approved