A393545 a(n) is the number of four-element sets of distinct integer-sided trapezoids whose base angles are 60 degrees of total area n^2 but which cannot fill an equilateral triangular grid of side n units.

0, 0, 0, 0, 0, 0, 15, 81, 220, 584, 1107, 2371, 3818, 7098, 10558, 17830, 24266, 40106, 50751, 79492, 100409, 146533, 176407, 266218, 302583, 429317, 506663, 696460, 774962

Offset

1,7

Comments

These sets consist of distinct integer-sided trapezoids formed within the equilateral triangular grid of side n units such that the total area is n^2.

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

Links

Table of n, a(n) for n=1..29.

Janaka Rodrigo, Python Code for 4-Trapezoid sets of total area n^2

Example

Sequence has 15 sets for n = 15:
 {(2 X 1), (4 X 1), (4 X 3), (5 X 4)},
 {(2 X 1), (5 X 1), (7 X 1), (7 X 2)},
 {(2 X 1), (5 X 1), (5 X 2), (5 X 3)},
 {(2 X 1), (4 X 2), (7 X 1), (5 X 3)},
 {(3 X 1), (4 X 1), (7 X 1), (7 X 2)},
 {(3 X 1), (4 X 1), (7 X 1), (5 X 4)},
 {(3 X 1), (3 X 2), (4 X 2), (5 X 4)},
 {(3 X 1), (3 X 2), (4 X 3), (5 X 3)},
 {(3 X 1), (5 X 1), (6 X 1), (7 X 2)},
 {(3 X 1), (6 X 1), (4 X 2), (5 X 3)},
 {(3 X 1), (6 X 1), (7 X 1), (6 X 2)},
 {(4 X 1), (5 X 1), (7 X 1), (6 X 2)},
 {(3 X 2), (4 X 2), (7 X 1), (5 X 2)},
 {(5 X 1), (6 X 1), (7 X 1), (5 X 2)},
 {(5 X 1), (4 X 2), (7 X 1), (4 X 3)}.
Therefore a(7) = 15.

Crossrefs

Cf. A389392, A389518, A390523, A391498, A391499, A393432.

Sequence in context: A102360 A375998 A372537 * A344722 A309336 A266288

Adjacent sequences: A393542 A393543 A393544 * A393546 A393547 A393548

Keyword

nonn,more

Author

Janaka Rodrigo, Feb 20 2026

Status

approved