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A382410
Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
4
6, 0, 30, 84, 546, 2310, 10710, 46284, 201066, 860700, 3676470, 15642594, 66461766, 282027720, 1196023110, 5069852964, 21485317146, 91036824270, 385700191830, 1634014069044, 6922219243506, 29324101445100, 124221795865230, 526219583239434, 2229121859293446, 9442763903572560
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OFFSET
0,1
REFERENCES
Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
LINKS
Table of n, a(n) for n=0..25.
Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas
Index entries for linear recurrences with constant coefficients, signature (6,-2,-29,16,40,-11,-14,2,1).
FORMULA
a(n) = (A382379(n,1) * A382379(n,2))/2.
a(n) = Lucas(n)*(Lucas(n) - 1)*(2*Lucas(n) - 1).
EXAMPLE
For n=3, the short leg is A382379(2,1) = 5 and the long leg is A382379(2,2) = 12 so the area is then a(3) = (5 * 12)/2 = 30.
MATHEMATICA
a=Table[LucasL[n], {n, 0, 30}]; Apply[Join, Map[{#(#-1)(2#-1)}&, a]]
CROSSREFS
Cf. A000032, A382379, A382409.
Sequence in context: A056462 A249869 A209446 * A375237 A047762 A186977
Adjacent sequences: A382407 A382408 A382409 * A382411 A382412 A382413
KEYWORD
nonn,easy
AUTHOR
Miguel-Ángel Pérez García-Ortega, Mar 24 2025
STATUS
approved

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Last modified April 12 15:50 EDT 2026. Contains 394616 sequences.
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