

A221838


Number of integer Heron triangles of height n.


3



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
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OFFSET

1,3


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.


FORMULA

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


EXAMPLE

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


PROG

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


CROSSREFS

Cf. A046079, A221837.
Sequence in context: A160762 A112968 A263407 * A338869 A104588 A157279
Adjacent sequences: A221835 A221836 A221837 * A221839 A221840 A221841


KEYWORD

nonn


AUTHOR

Eric M. Schmidt, Jan 27 2013


STATUS

approved



