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A221838
Number of integer Heron triangles of height n.
4
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
1,3
LINKS
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
Sequence in context: A112968 A263407 A377059 * A343122 A338869 A104588
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Jan 27 2013
STATUS
approved