A182640 a(n)=n+floor(r*a(n-1)), where r = golden ratio = (1+sqrt(5))/2, a(0)=0, a(1)=1.

0, 1, 3, 7, 15, 29, 52, 91, 155, 259, 429, 705, 1152, 1876, 3049, 4948, 8022, 12996, 21045, 34070, 55146, 89249, 144429, 233714, 378181, 611934, 990156, 1602133, 2592333, 4194511, 6786891, 10981451, 17768392, 28749895, 46518341, 75268291, 121786689, 197055039

Offset

0,3

Links

Table of n, a(n) for n=0..37.

Formula

a(n)=n+floor(r*a(n-1)), r=(1+sqrt(5))/2, a(0)=0, a(1)=1.

Mathematica

nxt[{n_, a_}]:={n+1, n+1+Floor[GoldenRatio*a]}; Join[{0}, Transpose[ NestList[ nxt, {1, 1}, 40]][[2]]] (* Harvey P. Dale, Apr 21 2013 *)

Crossrefs

Sequence in context: A364293 A009859 A322108 * A277643 A192960 A182717

Adjacent sequences: A182637 A182638 A182639 * A182641 A182642 A182643

Keyword

nonn

Author

Clark Kimberling, Nov 24 2010

Status

approved