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A383615 Length of the long leg of the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.

%I A383615 #20 Jul 20 2025 19:27:17
%S A383615 4,40,364,3444,34584,367224,4086940,47268364,564177640,6911470020,
%T A383615 86537568264,1103799334200,14305253278320,187980019758360,
%U A383615 2500329584942460,33615542888998620,456277454520102600,6246438361923425820,86175353763393711960,1197196443738946826760
%N A383615 Length of the long leg of the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.
%H A383615 Miguel-Ángel Pérez García-Ortega, <a href="/A383615/a383615.pdf">El Libro de las Ternas Pitagóricas</a>
%F A383615 a(n) = 2*C(n)*(C(n) - 1) where C(n) = A000108(n).
%e A383615 Triangles begin:
%e A383615   n=2:      3,     4,     5;
%e A383615   n=3:      9,    40,    41.
%e A383615 This sequence is column 2.
%Y A383615 Cf. A000108, A131428 (short leg), A383616 (semiperimeter), A381846 (area).
%K A383615 nonn,easy
%O A383615 2,1
%A A383615 _Miguel-Ángel Pérez García-Ortega_, May 02 2025