A063468 - OEIS

%I #17 Sep 08 2022 08:45:03

%S 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,

%T 20,22,22,22,22,24,26,26,28,28,30,32,34,34,34,34,36,36,36,36,36,40,42,

%U 44,46,46,48,48,48,50,50,52,54,54,54,54,62,62,62,64,64,66,66,66,68,70

%N 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.

%H Marius A. Burtea, <a href="/A063468/b063468.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 5 the Pythagorean triples are (3, 4, 5) and (4, 3, 5), so a (5) = 2.

%e For n = 10 the Pythagorean triples are (3, 4, 5), (4, 3, 5), (6, 8, 10) and (8, 6, 10), so a(10) = 4.

%e 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.

%t nq[n_] := SquaresR[2, n^2]/4 - 1; Accumulate@ Array[nq, 80] (* _Giovanni Resta_, Jan 23 2020 *)

%o (Magma) [#[<x,y,Floor(Sqrt(x^2+y^2))>: 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

%Y Cf. A062775, A211422.

%Y a(n) = 2*partial sums of A046080(n).

%K nonn

%O 1,5

%A Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 27 2001

%E Corrected and extended by _Vladeta Jovovic_, Jul 28 2001