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%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
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