A391499 a(n) is the least possible difference between the areas of the largest and smallest trapezoids in a 5 element set of distinct integer-sided trapezoids whose base angles are 60 degrees that fill an equilateral triangular grid of side n units.

8, 6, 7, 9, 8, 7, 9, 12, 11, 8, 11, 13, 16, 15, 10, 19, 11, 19, 15, 15, 22, 22, 21, 20, 18, 15, 29, 28, 24, 32, 21, 21, 21, 32, 35, 33, 34, 27, 37, 40, 45, 41, 25, 29, 45

Offset

6,1

Comments

Let the difference between the largest and smallest areas of the trapezoids be called the defect. Then a(n) is the minimum defect. The area of a trapezoid {b X s} is s*(2*b-s).

Links

Table of n, a(n) for n=6..50.

Janaka Rodrigo, Python code for minimum defects of five trapezoid sets

Example

For n = 6, there are two sets of trapezoids:
 {{2 X 1}, {3 X 1}, {3 X 2}, {5 X 1}, {6 X 1}} with defect = 11-3 = 8,
 {{2 X 1}, {3 X 1}, {4 X 1}, {5 X 1}, {7 X 2}} with defect = 12-3 = 9.
Therefore a(6) = 8.

Crossrefs

Cf. A390522 (minimum defect of 3 element sets), A390523 (minimum defect of 4 element sets), A391498 (5-element sets).

Sequence in context: A378968 A011465 A192409 * A159627 A302682 A384476

Adjacent sequences: A391496 A391497 A391498 * A391500 A391501 A391502

Keyword

nonn,more

Author

Janaka Rodrigo, Dec 17 2025

Extensions

a(42)-a(50) from Janaka Rodrigo, Mar 22 2026

Status

approved