cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A381483 Area of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

Original entry on oeis.org

6, 6, 30, 330, 6090, 153510, 4652340, 158459730, 5854550130, 229936985850, 9477338186316, 406314955623486, 18001068994899900, 820015284879972900, 38258577340819383240, 1822437624604345219170, 88405834606456644170370, 4358080082619077400555090, 217935771356984568896708700
Offset: 0

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Author

Keywords

Examples

			For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the area is then a(2) = (3 * 4 )/2 = 6.
		

References

  • Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Crossrefs

Programs

  • Mathematica
    a=Table[(2n)!/(n!(n+1)!),{n,0,18}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]

Formula

a(n) = (A383251(n,1) * A383251(n,2))/2.
a(n) = A000108(n)*(A000108(n) + 1)*(2*A000108(n) + 1).

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.

Original entry on oeis.org

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

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Author

Keywords

Examples

			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.
		

References

  • Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Crossrefs

Programs

  • Mathematica
    a=Table[Fibonacci[n],{n,0,30}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]

Formula

a(n) = (A382608(n,1) + A382608(n,2) + A382608(n,3))/2.
a(n) = (Fibonacci(n) + 1)*(2*Fibonacci(n) + 1).

A382610 Area of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

Original entry on oeis.org

0, 6, 6, 30, 84, 330, 1224, 4914, 19866, 82110, 341880, 1433790, 6034320, 25461774, 107592030, 455078910, 1925933100, 8153659170, 34527059160, 146226569946, 619340796690, 2623347596766, 11112097049136, 47070075918390, 199388054716704, 844610917608150, 3577801938273654, 15155740689781854, 64200560537978436
Offset: 0

Views

Author

Keywords

Examples

			For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the area is then a(2) = (3 * 4 )/2 = 6.
		

References

  • Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Crossrefs

Programs

  • Mathematica
    a=Table[Fibonacci[n],{n,0,28}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]

Formula

a(n) = (A382608(n,1) * A382608(n,2))/2.
a(n) = Fibonacci(n)*(Fibonacci(n) + 1)*(2*Fibonacci(n) + 1).

A382308 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

Original entry on oeis.org

1, 7, 7, 17, 31, 71, 161, 391, 967, 2449, 6271, 16199, 42049, 109511, 285767, 746641, 1952287, 5107207, 13364449, 34978247, 91557511, 239673617, 627429887, 1642561927, 4300168321, 11257801351, 29473006471, 77160847121, 202008934687, 528864985799, 1384584451361
Offset: 0

Views

Author

Keywords

Examples

			For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the sum of the legs is then a(2) = 3 + 4 = 7.
		

References

  • Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Crossrefs

Programs

  • Mathematica
    a=Table[Fibonacci[n],{n,0,30}];Apply[Join,Map[{2#^2+4#+1}&,a]]

Formula

a(n) = A382608(n,1) + A382608(n,2).
a(n) = 2*(Fibonacci(n))^2+4*Fibonacci(n) + 1.
Showing 1-4 of 4 results.