A050508 Golden rectangle numbers: n * A007067(n).

0, 2, 6, 15, 24, 40, 60, 77, 104, 135, 160, 198, 228, 273, 322, 360, 416, 476, 522, 589, 640, 714, 792, 851, 936, 1000, 1092, 1188, 1260, 1363, 1470, 1550, 1664, 1749, 1870, 1995, 2088, 2220, 2318, 2457, 2600, 2706, 2856, 3010, 3124, 3285, 3404, 3572, 3744

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 28 1999

Keywords

• easy
• nice
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007067.

Programs

Maple

A050508:=n->n*round(n*(1+sqrt(5))/2); seq(A050508(n), n=0..100); # Wesley Ivan Hurt, Nov 27 2013

Mathematica

a[n_] := n*Round[n*GoldenRatio]; Table[a[n], {n, 0, 48}] (* Jean-François Alcover, Jun 27 2012 *)

Python

from math import isqrt
def A050508(n): return n*((isqrt(5*n**2<<2)>>1)+n+1>>1) # Chai Wah Wu, Aug 29 2022