A384329 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000217(n) and its long leg and hypotenuse are consecutive natural numbers, n >= 0.
-1, 0, 1, 1, 0, 1, 5, 12, 13, 11, 60, 61, 19, 180, 181, 29, 420, 421, 41, 840, 841, 55, 1512, 1513, 71, 2520, 2521, 89, 3960, 3961, 109, 5940, 5941, 131, 8580, 8581, 155, 12012, 12013, 181, 16380, 16381, 209, 21840, 21841, 239, 28560, 28561, 271, 36720, 36721, 305, 46512, 46513, 341, 58140, 58141
Offset: 0
Examples
n=0: -1, 0, 1; n=1: 1, 0, 1; n=2: 5, 12, 13; n=3: 11, 60, 61; ...
Links
- José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas
Programs
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Mathematica
a=Table[(n(n+1))/2,{n,0,18}];Apply[Join,Map[{2#-1,2#^2-2#,2#^2-2#+1}&,a]]
Formula
row(n) = (2*T(n) - 1, 2*T(n)*(T(n) - 1), 2*T(n)*(T(n) - 1) + 1) where T(n) = A000217(n).
Comments