A337019 Maximum number of circles with unit area that can be packed into an equilateral triangle with an area of n.

0, 1, 1, 1, 3, 3, 4, 6, 6, 6, 7, 8, 10, 10, 10, 11, 12, 13, 15

Offset: 1

Author

Ya-Ping Lu, Nov 05 2020

Keywords

• nonn
• more

Comments

Are a(17) = 12 and a(18) = 13 proved? They look likely to be no more difficult to prove than some of the earlier terms, and are demonstrably lower bounds by the figures in the Friedman link. - Peter Munn, Apr 25 2023

The packing density, a(n)/n, approaches sqrt(3)*Pi/6 (approximately 0.9069) as n tends to infinity.

Links

• Erich Friedman, Circles in Triangles
• Wikipedia, Circle packing in an equilateral triangle

Crossrefs

Cf. A093766, A269110.

Formula

Limit_{n->oo} a(n)/n = A093766.

Extensions

Terms corrected by Andrew Howroyd and Peter Munn, Apr 23 2023