A382409
Semiperimeter 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.
Original entry on oeis.org
6, 1, 15, 28, 91, 231, 630, 1653, 4371, 11476, 30135, 79003, 207046, 542361, 1420455, 3719628, 9739491, 25500511, 66764790, 174798253, 457637131, 1198124676, 3136755615, 8212172403, 21499810566, 56287338481, 147362333055, 385799868028, 1010037606571, 2644313494551, 6922903755510
Offset: 0
For n=3, the short leg is A382379(2,1) = 5, the long leg is A382379(2,2) = 12 and the hypotenuse is A382379(2,3) = 13 so the semiperimeter is then a(3) = (5 + 12 + 13)/2 = 15.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
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a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(2#-1)}&,a]]
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.
Original entry on oeis.org
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
Offset: 0
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.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
- 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).
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a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
A383039
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000032(n) and its long leg and hypotenuse are consecutive natural numbers.
Original entry on oeis.org
7, 1, 17, 31, 97, 241, 647, 1681, 4417, 11551, 30257, 79201, 207367, 542881, 1421297, 3720991, 9741697, 25504081, 66770567, 174807601, 457652257, 1198149151, 3136795217, 8212236481, 21499914247, 56287506241, 147362604497, 385800307231, 1010038317217, 2644314644401, 6922905616007
Offset: 0
For n=3, the short leg is A382379(3,1) = 5 and the long leg is A382379(3,2) = 12 so the sum of the legs is then a(2) = 5 + 12 = 17.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
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a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{2#^2-1}&,a]]
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