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Maximum number of circles with unit area that can be packed into an equilateral triangle with an area of n.
5

%I #39 Apr 25 2023 11:17:02

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

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

%C 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

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

%H Erich Friedman, <a href="https://erich-friedman.github.io/packing/cirintri/">Circles in Triangles</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circle_packing_in_an_equilateral_triangle">Circle packing in an equilateral triangle</a>

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

%Y Cf. A093766, A269110.

%K nonn,more

%O 1,5

%A _Ya-Ping Lu_, Nov 05 2020

%E Terms corrected by _Andrew Howroyd_ and _Peter Munn_, Apr 23 2023