A178129 Partial sums of A050508.

0, 2, 8, 23, 47, 87, 147, 224, 328, 463, 623, 821, 1049, 1322, 1644, 2004, 2420, 2896, 3418, 4007, 4647, 5361, 6153, 7004, 7940, 8940, 10032, 11220, 12480, 13843, 15313, 16863, 18527, 20276, 22146, 24141, 26229, 28449, 30767, 33224, 35824, 38530

Offset: 0

Author

Jonathan Vos Post, May 20 2010

Keywords

• easy
• nonn

Comments

Partial sums of golden rectangle numbers. The subsequence

Examples

			a(19) = 0 + 2 + 6 + 15 + 24 + 40 + 60 + 77 + 104 + 135 +
		

Crossrefs

Cf. A000201, A007064, A026355, A007067, A050508.

Programs

Python

from math import isqrt
from itertools import count, islice
def A178129_gen(): # generator of terms
    return accumulate(n*((isqrt(5*n**2<<2)>>1)+n+1>>1) for n in count(0))
A178129_list = list(islice(A178129_gen(),10)) # Chai Wah Wu, Aug 29 2022

Formula

a(n) = Sum_{i=0..n} A050508(i) = Sum_{i=0..n} (i*A007067(i)).