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URL: https://oeis.org/A382609

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A382609
Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
4
1, 6, 6, 15, 28, 66, 153, 378, 946, 2415, 6216, 16110, 41905, 109278, 285390, 746031, 1951300, 5105610, 13361865, 34974066, 91550746, 239662671, 627412176, 1642533270, 4300121953, 11257726326, 29472885078, 77160650703, 202008616876, 528864471570, 1384583619321
OFFSET
0,2
REFERENCES
Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
LINKS
Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas.
FORMULA
a(n) = (A382608(n,1) + A382608(n,2) + A382608(n,3))/2.
a(n) = (Fibonacci(n) + 1)*(2*Fibonacci(n) + 1).
G.f.: (1 + 2*x - 16*x^2 + 9*x^3 + 12*x^4 - 6*x^5)/((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - Andrew Howroyd, Nov 13 2025
EXAMPLE
For n=2, the short leg is A382608(2,1) = 3, the long leg is A382608(2,2) = 4 and the hypotenuse is A382608(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
MATHEMATICA
a=Table[Fibonacci[n], {n, 0, 30}]; Apply[Join, Map[{(#+1)(2#+1)}&, a]]
PROG
(PARI) a(n) = (fibonacci(n) + 1)*(2*fibonacci(n) + 1); \\ Andrew Howroyd, Nov 13 2025
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved