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

0,2

Links

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

Formula

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

Prog

(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

Crossrefs

Cf. A005875.

Sequence in context: A338536 A090073 A327089 * A232385 A275155 A259634

Adjacent sequences: A016725 A016726 A016727 * A016729 A016730 A016731

Keyword

nonn

Author

csvcjld(AT)nomvst.lsumc.edu

Status

approved