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A382843 Length of the long leg in the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.

%I A382843 #18 Jul 16 2025 19:01:52
%S A382843 0,0,0,4,12,40,112,312,840,2244,5940,15664,41184,108112,283504,742980,
%T A382843 1946364,5097624,13348944,34953160,91516920,239607940,627323620,
%U A382843 1642389984,4299890112,11257351200,29472278112,77159668612,202007027820,528861900424,1384579459120
%N A382843 Length of the long leg in the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
%H A382843 Miguel-Ángel Pérez García-Ortega, <a href="/A382843/a382843.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382843 a(n) = 2*A000045(n)*(A000045(n) - 1),.
%e A382843 Triples begin:
%e A382843   n=0:     -1,     0,     1;
%e A382843   n=1:      1,     0,     1;
%e A382843   n=2:      1,     0,     1;
%e A382843   n=3:      3,     4,     5.
%e A382843 This sequence gives column 2.
%Y A382843 Cf. A000045, A382844 (area), A382845 (sum of the legs), A095122 (semiperimeter), A001595 (short leg).
%K A382843 sign,easy
%O A382843 0,4
%A A382843 _Miguel-Ángel Pérez García-Ortega_, Apr 06 2025