A382843 Length of the long leg in the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.

0, 0, 0, 4, 12, 40, 112, 312, 840, 2244, 5940, 15664, 41184, 108112, 283504, 742980, 1946364, 5097624, 13348944, 34953160, 91516920, 239607940, 627323620, 1642389984, 4299890112, 11257351200, 29472278112, 77159668612, 202007027820, 528861900424, 1384579459120

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Apr 06 2025

Keywords

• sign
• easy

Examples

			Triples begin:
  n=0:     -1,     0,     1;
  n=1:      1,     0,     1;
  n=2:      1,     0,     1;
  n=3:      3,     4,     5.
This sequence gives column 2.
		

Links

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

Crossrefs

Cf. A000045, A382844 (area), A382845 (sum of the legs), A095122 (semiperimeter), A001595 (short leg).

Formula

a(n) = 2*A000045(n)*(A000045(n) - 1),.