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A178129
Partial sums of A050508.
0
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
0,2
COMMENTS
Partial sums of golden rectangle numbers. The subsequence
FORMULA
a(n) = Sum_{i=0..n} A050508(i) = Sum_{i=0..n} (i*A007067(i)).
EXAMPLE
a(19) = 0 + 2 + 6 + 15 + 24 + 40 + 60 + 77 + 104 + 135 +
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 20 2010
STATUS
approved