A390522 a(n) is the least possible difference between the areas of the largest and smallest trapezoids in a 3 element set of distinct integer-sided trapezoids whose base angles are 60 degrees, that fill an equilateral triangular grid of side n units.

5, 7, 11, 9, 11, 17, 13, 15, 23, 17, 19, 29, 21, 23, 35, 25, 27, 41, 29, 31, 47, 33, 35, 53, 37, 39, 59, 41, 43, 65, 45, 47, 71, 49, 51, 77, 53, 55, 83, 57, 59, 89, 61, 63, 95, 65, 67, 101, 69, 71, 107, 73, 75, 113, 77, 79, 113, 81, 83, 125, 85, 87, 131, 89, 91, 137, 93, 95, 143, 97, 99, 149

Offset

4,1

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=4..75.

Example

For n = 6, there is only one set of trapezoids: {{3 X 1}, {4 X 3}, {5 X 2}} with defect = 16 - 5 = 11. Therefore a(6) = 11, since this is the minimum defect.

Crossrefs

Cf. A389392, A389518.

Sequence in context: A023594 A357099 A277777 * A254930 A317769 A104200

Adjacent sequences: A390519 A390520 A390521 * A390523 A390524 A390525

Keyword

nonn

Author

Janaka Rodrigo, Nov 09 2025

Status

approved