A075312 Products of Wythoff pairs: [n*r]*[n*r^2], where [] is the floor function and r is the golden ratio, (1+sqrt(5))/2.

2, 15, 28, 60, 104, 135, 198, 240, 322, 416, 476, 589, 714, 792, 936, 1025, 1188, 1363, 1470, 1664, 1782, 1995, 2220, 2356, 2600, 2856, 3010, 3285, 3450, 3744, 4050, 4233, 4558, 4895, 5096, 5452, 5664, 6039, 6426, 6656, 7062, 7303, 7728, 8165, 8424, 8880

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = A000201(n) * A001950(n) = floor(n*r)*(n+floor(n*r)), where r=(1+sqrt(5))/2.

Example

Wythoff pairs:  (1,2), (3,5), (4,7), (6,10),..., so that
A075312 = (1*2, 3*5, 4*7, 6*10,...).

Prog

(Python)
from math import isqrt
def A075312(n): return (lambda m: m*(m+n))(n+isqrt(5*n**2)>>1) # Chai Wah Wu, Aug 29 2022

Crossrefs

The pairs are (A000201(n), A001950(n)). The sum is given by A003623.

Sequence in context: A370031 A338457 A153080 * A212975 A128828 A032002

Adjacent sequences: A075309 A075310 A075311 * A075313 A075314 A075315

Keyword

nonn

Author

Amarnath Murthy, Sep 13 2002

Status

approved