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URL: https://oeis.org/A382114

⇱ A382114 - OEIS


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A382114
Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
4
6, 6, 15, 66, 435, 3655, 35245, 369370, 4094091, 47292675, 564261621, 6911763951, 86538608325, 1103803048701, 14305266650521, 187980068232586, 2500329761730811, 33615543537222571, 456277456908296101, 6246438370759741771, 86175353796214314061, 1197196443861278161861, 16738118900567747790121, 235379797036403711485951
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
FORMULA
a(n) = (A383251(n,1) + A383251(n,2) + A383251(n,3))/2.
a(n) = (A000108(n) + 1)*(2*A000108(n) + 1).
EXAMPLE
For n=2, the short leg is A383251(2,1) = 3, the long leg is A383251(2,2) = 4 and the hypotenuse is A383251(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
MATHEMATICA
a=Table[(2n)!/(n!(n+1)!), {n, 0, 23}]; Apply[Join, Map[{(#+1)(2#+1)}&, a]]
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved