A382379 Length of the long leg in the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

4, 0, 12, 24, 84, 220, 612, 1624, 4324, 11400, 30012, 78804, 206724, 541840, 1419612, 3718264, 9737284, 25496940, 66759012, 174788904, 457622004, 1198100200, 3136716012, 8212108324, 21499706884, 56287170720, 147362061612, 385799428824, 1010036895924

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Mar 24 2025

Keywords

• nonn
• easy

Examples

			The triangles begin:
  n=0:      3,     4,     5;
  n=1:      1,     0,     1;
  n=2:      5,    12,    13;
  n=3:      7,    24,    25;
  ...
This sequence gives the middle column
		

Links

• Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Crossrefs

Cf. A000032, A022319 (short leg), A382409 (semiperimeter), A382410 (area).

Formula

a(n) = 2*A000032(n)*(A000032(n) - 1).