A304035 a(n) is the number of lattice points inside a square bounded by the lines x=-n/sqrt(2), x=n/sqrt(2), y=-n/sqrt(2), y=n/sqrt(2).

1, 9, 25, 25, 49, 81, 81, 121, 169, 225, 225, 289, 361, 361, 441, 529, 625, 625, 729, 841, 841, 961, 1089, 1089, 1225, 1369, 1521, 1521, 1681, 1849, 1849, 2025, 2209, 2401, 2401, 2601, 2809, 2809, 3025, 3249, 3249, 3481, 3721, 3969, 3969, 4225, 4489, 4489, 4761, 5041, 5329, 5329, 5625, 5929, 5929

Offset

1,2

Comments

If we calculate the first difference of this sequence and then substitute nonzero numbers as 1, we get exactly A080764.

If we include boundary points of the squares we get same sequence (obviously).

Duplicates appear at 4, 7, 11, 14, 18, 21, 24, 28, 31, 35, 38, 41, 45, 48, 52, 55 (= A083051 ?). - Robert G. Wilson v, Jun 20 2018

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = A051132(n) - A303642(n).

Prog

(Python)
import math
for n in range (1, 100):
.count=0
.for x in range (-n, n):
..for y in range (-n, n):
...if ((2*x*x < n*n) and (2*y*y < n*n)):
....count=count+1
.print(count)
(PARI) a(n) = sum(x=-n, n, sum(y=-n, n, ((2*x^2 < n^2) && (2*y^2 < n^2)))); \\ Michel Marcus, May 22 2018

Crossrefs

Cf. A080764, A049472, A051132, A303642.

Sequence in context: A282176 A204918 A322999 * A339726 A155109 A268576

Adjacent sequences: A304032 A304033 A304034 * A304036 A304037 A304038

Keyword

nonn

Author

Kirill Ustyantsev, May 05 2018

Status

approved