A338202 a(n) is the number of unit perimeter triangles with rational side lengths whose largest denominator is less than or equal to n.

0, 0, 1, 1, 2, 2, 4, 5, 7, 8, 12, 14, 19, 21, 26, 30, 38, 42, 52, 60, 70, 76, 90, 98, 113, 122, 138, 152, 173, 186, 210, 226, 249, 265, 306, 324, 357, 377, 410, 442, 482, 514, 558, 592, 645, 675, 727, 759, 813, 848, 902, 950, 1015, 1053, 1140, 1210, 1277, 1326

Offset: 1

Author

Peter Kagey, Oct 16 2020

Keywords

• nonn

Comments

Partial sums of A338201.

a(n) is bounded above by A180360(n,3).

Examples

			For n = 8, the a(8) = 5 triangles have side lengths
1/3, 1/3, 1/3;
1/5, 2/5, 2/5;
2/7, 2/7, 3/7;
1/7, 3/7, 3/7; and
1/4, 3/8, 3/8.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A180360, A338201.