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A382608 Long leg of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

%I A382608 #21 Jul 13 2025 23:17:42
%S A382608 4,4,12,24,60,144,364,924,2380,6160,16020,41760,109044,285012,745420,
%T A382608 1950312,5104012,13359280,34969884,91543980,239651724,627394464,
%U A382608 1642504612,4300075584,11257651300,29472763684,77160454284,202008299064,528863957340,1384582787280
%N A382608 Long leg of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%H A382608 Miguel-Ángel Pérez García-Ortega, <a href="/A382608/a382608.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382608 a(n) = 2*F(n)*(F(n) + 1) where F(n) = A000045(n).
%e A382608 Triangle begins:
%e A382608   n=1:      3,    4,    5;
%e A382608   n=2:      3,    4,    5;
%e A382608   n=3:      5,   12,   13;
%e A382608 where this sequence is the middle column.
%t A382608 a=Table[Fibonacci[n],{n,0,16}];Apply[Join,Map[{2#+1,2#^2+2#,2#^2+2#+1}&,a]]
%Y A382608 Cf. A000045 (inradius), A001588 (short leg), A382609 (semiperimeter), A382610 (area).
%K A382608 nonn,easy
%O A382608 1,1
%A A382608 _Miguel-Ángel Pérez García-Ortega_, Mar 31 2025