

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
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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



FORMULA



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



KEYWORD

nonn


AUTHOR



STATUS

approved



