A394528 a(n) is the number of 5 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, 0, 2, 20, 78, 183, 396, 679, 1184, 1793, 2681, 3905, 5476, 7342, 9841, 12643, 16361, 20632, 25618, 31333, 38572, 46294, 55370, 65821, 77654, 90550, 105957, 122215, 140769, 160753, 183771, 208807, 236599, 265853, 298694, 334002, 373769, 414686, 461062

Offset

1,6

Comments

A trapezoid whose base angles are 60 degrees with larger base b and legs s is denoted by {b X s} in 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 A391498.

Links

Table of n, a(n) for n=1..42.

Janaka Rodrigo, Python Code for five element sets of trapezoids of distinct areas

Formula

a(n) <= A391498(n).

Example

When n = 8, A391498 has 83 sets of distinct trapezoids and following 5 sets which contain trapezoids with equal area are removed to obtain 78 sets:
 {{6 X 1}, {8 X 1}, {4 X 3}, {5 X 2}, {4 X 1}},
 {{6 X 1}, {8 X 1}, {4 X 3}, {6 X 2}, {2 X 1}},
 {{7 X 1}, {8 X 1}, {4 X 3}, {5 X 2}, {3 X 1}},
 {{8 X 1}, {4 X 3}, {6 X 2}, {3 X 1}, {5 X 1}},
 {{8 X 1}, {4 X 3}, {7 X 2}, {2 X 1}, {4 X 1}}.
Therefore a(8) = 78.

Crossrefs

Cf. A391498, A389518.

Sequence in context: A259110 A135188 A161007 * A391498 A331760 A098077

Adjacent sequences: A394525 A394526 A394527 * A394529 A394530 A394531

Keyword

nonn

Author

Janaka Rodrigo, Mar 23 2026

Status

approved