A382844
Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
Original entry on oeis.org
0, 0, 0, 6, 30, 180, 840, 3900, 17220, 75174, 323730, 1386264, 5909904, 25136040, 106739256, 452846310, 1920088086, 8138356716, 34486996824, 146121685380, 619066205340, 2622628707270, 11110214972010, 47065148576496, 199375154768160, 844577145104400, 3577713520710960
Offset: 0
For n=4, the short leg is A382843(2,1) = 3 and the long leg is A382843(2,2) = 4 so the area is then a(4) = (3 * 4)/2 = 6.
- 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[Fibonacci[n],{n,0,26}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
A382845
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
Original entry on oeis.org
-1, 1, 1, 7, 17, 49, 127, 337, 881, 2311, 6049, 15841, 41471, 108577, 284257, 744199, 1948337, 5100817, 13354111, 34961521, 91530449, 239629831, 627359041, 1642447297, 4299982847, 11257501249, 29472520897, 77160061447, 202007663441, 528862928881, 1384581123199
Offset: 0
For n=4, the short leg is A382843(2,1) = 3 and the long leg is A382843(2,2) = 4 so the sum of the legs is then a(4) = 3 + 4 = 7.
- 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[Fibonacci[n],{n,0,30}];Apply[Join,Map[{2#^2-1}&,a]]
A095122
a(n) = Fibonacci(n)*(2*Fibonacci(n)-1).
Original entry on oeis.org
0, 1, 1, 6, 15, 45, 120, 325, 861, 2278, 5995, 15753, 41328, 108345, 283881, 743590, 1947351, 5099221, 13351528, 34957341, 91523685, 239618886, 627341331, 1642418641, 4299936480, 11257426225, 29472399505, 77159865030, 202007345631, 528862414653, 1384580291160
Offset: 0
- 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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#(2#-1)&/@Fibonacci[Range[0,30]] (* or *) LinearRecurrence[{3,1,-5,-1,1},{0,1,1,6,15},30] (* Harvey P. Dale, Jan 14 2012 *)
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