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 A063468 Number of Pythagorean triples in the range [1..n], i.e., the number of integer solutions to x^2 + y^2 = z^2 with 1 <= x,y,z <= n. 2
 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 4, 4, 6, 6, 8, 8, 10, 10, 10, 12, 12, 12, 12, 12, 16, 18, 18, 18, 20, 22, 22, 22, 22, 24, 26, 26, 28, 28, 30, 32, 34, 34, 34, 34, 36, 36, 36, 36, 36, 40, 42, 44, 46, 46, 48, 48, 48, 50, 50, 52, 54, 54, 54, 54, 62, 62, 62, 64, 64, 66, 66, 66, 68, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Marius A. Burtea, Table of n, a(n) for n = 1..1000 EXAMPLE For n = 5 the Pythagorean triples are (3, 4, 5) and (4, 3, 5), so a (5) = 2. For n = 10 the Pythagorean triples are (3, 4, 5), (4, 3, 5), (6, 8, 10) and (8, 6, 10), so a(10) = 4. For n = 17 the Pythagorean triples are (3, 4, 5), (4, 5, 3), (5, 12, 13), (12, 5, 13), (6, 8, 10), (8, 6, 10), (8, 15, 17), (15, 8, 17), (9, 12, 15) and (12, 9, 15), so a(17) = 10. MATHEMATICA nq[n_] := SquaresR[2, n^2]/4 - 1; Accumulate@ Array[nq, 80] (* Giovanni Resta, Jan 23 2020 *) PROG (Magma) [#[: x in [1..n], y in [1..n]| IsSquare(x^2+y^2) and Floor(Sqrt(x^2+y^2)) le n]:n in [1..74]]; // Marius A. Burtea, Jan 22 2020 CROSSREFS Cf. A062775, A211422. a(n) = 2*partial sums of A046080(n). Sequence in context: A260984 A108105 A321213 * A010336 A054537 A029104 Adjacent sequences: A063465 A063466 A063467 * A063469 A063470 A063471 KEYWORD nonn AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 27 2001 EXTENSIONS Corrected and extended by Vladeta Jovovic, Jul 28 2001 STATUS approved

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Last modified March 31 17:18 EDT 2023. Contains 361668 sequences. (Running on oeis4.)