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Three-column table read by rows giving Pythagorean triples [a,b,c] that are the (constant) differences between consecutive triples in rows of A338275.
3

%I #23 Dec 15 2021 11:39:36

%S 0,4,4,6,8,10,0,16,16,16,12,20,10,24,26,0,36,36,30,16,34,24,32,40,14,

%T 48,50,0,64,64,48,20,52,42,40,58,32,60,68,18,80,82,0,100,100,70,24,74,

%U 64,48,80,54,72,90,40,96,104,22,120,122,0,144,144

%N Three-column table read by rows giving Pythagorean triples [a,b,c] that are the (constant) differences between consecutive triples in rows of A338275.

%H David Lovler, <a href="/A338895/b338895.txt">Table of n, a(n) for n = 1..300</a>

%H David Lovler, <a href="/A338895/a338895.txt">Triples for m up to 100</a>

%F a = ((m-1)^2 - n^2)/2, b = (m-1)*n, c = ((m-1)^2 + n^2)/2, where m and n generate the A338275 row in question.

%e The table begins:

%e [ 0, 4, 4],

%e [ 6, 8, 10],

%e [ 0, 16, 16],

%e [16, 12, 20],

%e [10, 24, 26],

%e [ 0, 36, 36],

%e [30, 16, 34],

%e [24, 32, 40],

%e [14, 48, 50],

%e [ 0, 64, 64],

%e [48, 20, 52],

%e [42, 40, 58],

%e [32, 60, 68],

%e [18, 80, 82],

%e [ 0, 100, 100],

%e [70, 24, 74],

%e [64, 48, 80],

%e [54, 72, 90],

%e [40, 96, 104],

%e [22, 120, 122],

%e [ 0, 144, 144],

%e ...

%t Table[{((#1 - 1)^2 - #2^2)/2, (#1 - 1) #2, ((#1 - 1)^2 + #2^2)/2} & @@ {m, n}, {m, 3, 13, 2}, {n, 2, m, 2}] // Flatten (* _Michael De Vlieger_, Dec 04 2020 *)

%o (PARI) lista(mm) = {forstep (m=3, mm, 2, forstep (n=2, m, 2, print([((m-1)^2 - n^2)/2, (m-1)*n, ((m-1)^2 + n^2)/2]);););} \\ _Michel Marcus_, Dec 04 2020

%Y Cf. A338275, A338896.

%K nonn,tabf

%O 1,2

%A _David Lovler_, Nov 14 2020