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A328499
The number of primitive Pythagorean triangles with perimeter less than n.
1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
OFFSET
1,30
COMMENTS
D. N. Lehmer has proved that the asymptotic density of a(n) is a(n)/n = log(2)/Pi^2 = 0.07023049... See A118858.
EXAMPLE
For n=90, the triples are
{3, 4, 5}, 3 + 4 + 5 = 12 < 90
{5, 12, 13}, 5 + 12 + 13 = 30 < 90
{7, 24, 25}, 7 + 24 + 25 = 56 < 90
{8, 15, 17}, 8 + 15 + 17 = 40 < 90
{9, 40, 41}, 9 + 40 + 41 = 90
{12, 35, 37}, 12 + 35 + 37 = 84 < 90
{20, 21, 29}, 20 + 21 + 29 = 70 < 90
so a(90)=7.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mo Li, Oct 17 2019
STATUS
approved