A392330 a(n) is the number of 5 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, 2, 65, 373, 1472, 4150, 10977, 23698, 51195, 95225, 181674, 304509, 538484, 834615, 1381950

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..20.

Example

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

Crossrefs

Cf. A389392, A389518, A390523, A391498, A391499, A393545, A393432.

Sequence in context: A041511 A156651 A342608 * A294179 A002604 A382433

Adjacent sequences: A392327 A392328 A392329 * A392331 A392332 A392333

Keyword

nonn,more

Author

Janaka Rodrigo, Mar 01 2026

Extensions

a(16)-a(20) from Sean A. Irvine, Mar 09 2026

Status

approved