A389518 a(n) is the number of 4 element sets of integer sided trapezoids with distinct areas and base angles that are 60 degrees, which fill an equilateral triangular grid of side n units.

0, 0, 0, 0, 1, 9, 20, 36, 62, 99, 136, 203, 264, 349, 455, 574, 709, 866, 1035, 1249, 1470, 1707, 1979, 2302, 2636, 2983, 3386, 3826, 4277, 4789, 5325, 5903, 6472, 7166, 7879, 8620, 9383, 10232, 11074, 12070, 13027, 14071, 15151, 16285, 17510, 18731, 20039, 21449, 22889, 24391

Offset

1,6

Comments

A trapezoid whose base angles are 60 degrees with longer base b and legs s is denoted by {b X s} in the examples and has area s*(2b - s) times that of a unit equilateral triangle.

This is the sequence generated by removing sets containing trapezoids of equal areas from the sequence A389392.

Links

Janaka Rodrigo, Table of n, a(n) for n = 1..75

Janaka Rodrigo, Category B Distinct Sets and Sets of Distinct Areas

Janaka Rodrigo, Category A Distinct Sets and Sets of Distinct Areas

Formula

a(n) <= A389392(n).

Example

When n = 8, A389392 has 40 sets of distinct trapezoids and the following 4 sets which contains trapezoids with equal area are removed to obtain 36 sets:
   {{2 X 1}, {7 X 1}, {7 X 2}, {5 X 4}},
   {{3 X 1}, {6 X 1}, {7 X 2}, {5 X 4}},
   {{4 X 1}, {5 X 1}, {7 X 2}, {5 X 4}},
   {{4 X 1}, {8 X 1}, {4 X 3}, {5 X 3}}.

Crossrefs

Cf. A389392.

Sequence in context: A147479 A146680 A143704 * A128153 A389392 A249044

Adjacent sequences: A389515 A389516 A389517 * A389519 A389520 A389521

Keyword

nonn

Author

Janaka Rodrigo, Oct 07 2025

Status

approved