cp's OEIS Frontend

A338895 Three-column table read by rows giving Pythagorean triples [a,b,c] that are the (constant) differences between consecutive triples in rows of A338275.

%I A338895 #23 Dec 15 2021 11:39:36
%S A338895 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 A338895 48,50,0,64,64,48,20,52,42,40,58,32,60,68,18,80,82,0,100,100,70,24,74,
%U A338895 64,48,80,54,72,90,40,96,104,22,120,122,0,144,144
%N A338895 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 A338895 David Lovler, <a href="/A338895/b338895.txt">Table of n, a(n) for n = 1..300</a>
%H A338895 David Lovler, <a href="/A338895/a338895.txt">Triples for m up to 100</a>
%F A338895 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 A338895 The table begins:
%e A338895   [ 0,   4,   4],
%e A338895   [ 6,   8,  10],
%e A338895   [ 0,  16,  16],
%e A338895   [16,  12,  20],
%e A338895   [10,  24,  26],
%e A338895   [ 0,  36,  36],
%e A338895   [30,  16,  34],
%e A338895   [24,  32,  40],
%e A338895   [14,  48,  50],
%e A338895   [ 0,  64,  64],
%e A338895   [48,  20,  52],
%e A338895   [42,  40,  58],
%e A338895   [32,  60,  68],
%e A338895   [18,  80,  82],
%e A338895   [ 0, 100, 100],
%e A338895   [70,  24,  74],
%e A338895   [64,  48,  80],
%e A338895   [54,  72,  90],
%e A338895   [40,  96, 104],
%e A338895   [22, 120, 122],
%e A338895   [ 0, 144, 144],
%e A338895   ...
%t A338895 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 A338895 (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 A338895 Cf. A338275, A338896.
%K A338895 nonn,tabf
%O A338895 1,2
%A A338895 _David Lovler_, Nov 14 2020