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A304035
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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).
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0
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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
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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