This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321769 #13 Dec 01 2018 04:54:12 %S A321769 4,12,20,8,24,48,28,80,120,36,56,72,12,40,88,60,208,304,84,168,224,44, %T A321769 176,336,180,456,696,220,288,360,52,140,252,120,252,396,136,132,156, %U A321769 16,60,140,104,396,572,152,340,460,96,468,884,464,1140,1748,560,700 %N A321769 Consider the tree of triples P(n, k) with n > 0 and 0 < k <= 3^(n-1), such that P(1, 1) = [3; 4; 5] and each triple t on some row branches to the triples A*t, B*t, C*t on the next row (with A = [1, -2, 2; 2, -1, 2; 2, -2, 3], B = [1, 2, 2; 2, 1, 2; 2, 2, 3] and C = [-1, 2, 2; -2, 1, 2; -2, 2, 3]); T(n, k) is the second component of P(n, k). %C A321769 The tree P runs uniquely through every primitive Pythagorean triple. %C A321769 See A321768 for additional comments about P. %C A321769 All terms are even. %H A321769 Rémy Sigrist, <a href="/A321769/b321769.txt">Rows n = 1..9, flattened</a> %H A321769 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples">Tree of primitive Pythagorean triples</a> %H A321769 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a> %F A321769 Empirically: %F A321769 - T(n, 1) = A046092(n), %F A321769 - T(n, (3^(n-1) + 1)/2) = A046729(n), %F A321769 - T(n, 3^(n-1)) = 4 * n. %e A321769 The first rows are: %e A321769 4 %e A321769 12, 20, 8 %e A321769 24, 48, 28, 80, 120, 36, 56, 72, 12 %o A321769 (PARI) M = [[1, -2, 2; 2, -1, 2; 2, -2, 3], [1, 2, 2; 2, 1, 2; 2, 2, 3], [-1, 2, 2; -2, 1, 2; -2, 2, 3]]; %o A321769 T(n, k) = my (t=[3; 4; 5], d=digits(3^(n-1)+k-1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (t[2, 1]) %Y A321769 See A321768 and A321770 for the other components. %Y A321769 Cf. A046092, A046729. %K A321769 nonn,tabf %O A321769 1,1 %A A321769 _Rémy Sigrist_, Nov 18 2018