A338201 a(n) is the number of unit perimeter triangles with rational side lengths whose largest denominator is equal to n.

0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 4, 2, 5, 2, 5, 4, 8, 4, 10, 8, 10, 6, 14, 8, 15, 9, 16, 14, 21, 13, 24, 16, 23, 16, 41, 18, 33, 20, 33, 32, 40, 32, 44, 34, 53, 30, 52, 32, 54, 35, 54, 48, 65, 38, 87, 70, 67, 49, 80, 64, 85, 56, 116, 64, 116, 73, 102, 80, 96, 99

Offset

1,7

Comments

Records occur at n=1, 3, 7, 11, 13, 17, 19, 23, 25, 27, 29, 31, 35, 43, 45, 49, 53, 55, 63, 73, 75, 77, 91, 99, 105, 117, 133, 143, 175, 187, ...

Links

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

Code Golf Stack Exchange, Triangles with rational side lengths

Peter Kagey, Haskell program.

Example

For n = 20, the a(20) = 8 triangles have sides:
1/4,  7/20, 2/5;
1/12, 9/20, 7/15;
3/10, 7/20, 7/20;
3/20, 2/5,  9/20;
1/4,  3/10, 9/20;
2/15, 5/12, 9/20;
1/5,  7/20, 9/20; and
1/10, 9/20, 9/20.

Crossrefs

Cf. A180360, A338202.

Sequence in context: A187718 A029196 A051493 * A029173 A002331 A060805

Adjacent sequences: A338198 A338199 A338200 * A338202 A338203 A338204

Keyword

nonn

Author

Peter Kagey, Oct 16 2020

Status

approved