A016728 Number of integer points (x,y,z) at distance <= 0.5 from sphere of radius n.

1, 18, 62, 98, 210, 350, 450, 602, 762, 1142, 1250, 1458, 1814, 2178, 2498, 2622, 3338, 3722, 4170, 4358, 5034, 5714, 5982, 6602, 7130, 8034, 8606, 9066, 9962, 10550, 11226, 12146, 12606, 13802, 14754, 15194, 16454, 17154, 18266, 18750

Offset: 0

Author

csvcjld(AT)nomvst.lsumc.edu

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005875.

Programs

Python

from itertools import combinations_with_replacement
from math import prod
from collections import Counter
def A016728(n):
    if n == 0: return 1
    x, y = (2*n-1)**2, (2*n+1)**2
    return sum(6//prod((1,1,2,6)[d] for d in q.values())<<3-q[0] for q in map(Counter,combinations_with_replacement(range(n+1),3)) if x <= sum(b*a**2 for a, b in q.items())<<2 <= y) # Chai Wah Wu, Jun 20 2024

Python

# uses Python code from A005875
def A016728(n):
    if n == 0: return 1
    return sum(A005875(i) for i in range(n*(n-1)+1,n*(n+1)+1)) # Chai Wah Wu, Jun 23 2024

Formula

For n > 0, a(n) = Sum_{i=n*(n-1)+1..n*(n+1)} A005875(i). - Chai Wah Wu, Jun 23 2024