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

1,5

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

Table of n, a(n) for n=1..19.

Erich Friedman, Circles in Triangles

Wikipedia, Circle packing in an equilateral triangle

Formula

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

Crossrefs

Cf. A093766, A269110.

Sequence in context: A074883 A338015 A196245 * A092200 A130481 A145805

Adjacent sequences: A337016 A337017 A337018 * A337020 A337021 A337022

Keyword

nonn,more

Author

Ya-Ping Lu, Nov 05 2020

Extensions

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

Status

approved