A180360 -id:A180360 - cp's OEIS frontend

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

Peter Kagey, Oct 16 2020

nonn

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, ...

			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.

Peter Kagey, Table of n, a(n) for n = 1..300
Code Golf Stack Exchange, Triangles with rational side lengths
Peter Kagey, Haskell program.

Cf. A180360, A338202.

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

Original entry on oeis.org

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

Peter Kagey, Oct 16 2020

nonn

Partial sums of A338201.

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

			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.

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

Cf. A180360, A338201.

cp's OEIS Frontend

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

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