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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A155109 A268576 A053850

Adjacent sequences:  A304032 A304033 A304034 * A304036 A304037 A304038

KEYWORD

nonn

AUTHOR

Kirill Ustyantsev, May 05 2018

STATUS

approved

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Last modified August 11 04:03 EDT 2020. Contains 336421 sequences. (Running on oeis4.)