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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 * A339726 A155109 A268576 Adjacent sequences: A304032 A304033 A304034 * A304036 A304037 A304038 KEYWORD nonn AUTHOR Kirill Ustyantsev, May 05 2018 STATUS approved

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Last modified July 12 17:26 EDT 2024. Contains 374251 sequences. (Running on oeis4.)