A221838 Number of integer Heron triangles of height n.

0, 0, 2, 2, 2, 2, 2, 6, 6, 2, 2, 20, 2, 2, 20, 12, 2, 6, 2, 20, 20, 2, 2, 56, 6, 2, 12, 20, 2, 20, 2, 20, 20, 2, 20, 56, 2, 2, 20, 56, 2, 20, 2, 20, 56, 2, 2, 110, 6, 6, 20, 20, 2, 12, 20, 56, 20, 2, 2, 182, 2, 2, 56, 30, 20, 20, 2, 20, 20, 20, 2, 156, 2, 2

Offset: 1

Author

Eric M. Schmidt, Jan 27 2013

Keywords

• nonn

Examples

			For n = 3, the two triangles have side lengths (3, 4, 5) and (5, 5, 8), with areas 6 and 12 respectively.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..10000
• Sourav Sen Gupta, Nirupam Kar, Subhamoy Maitra, Santanu Sarkar, and Pantelimon Stanica, Counting Heron triangles with Constraints, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A3, 2013.
• Eric Weisstein's World of Mathematics, Heronian Triangle.

Crossrefs

Cf. A046079, A221837.

Programs

Sage

def A221838(n) : pyth = (number_of_divisors(n^2 if n%2==1 else (n/2)^2) - 1) // 2; return pyth^2 + pyth

Formula

a(n) = A221837(n) + A046079(n) = A046079(n)^2 + A046079(n).