A373732 a(n) = floor(4*n^2/sqrt(3)).

0, 2, 9, 20, 36, 57, 83, 113, 147, 187, 230, 279, 332, 390, 452, 519, 591, 667, 748, 833, 923, 1018, 1117, 1221, 1330, 1443, 1561, 1683, 1810, 1942, 2078, 2219, 2364, 2514, 2669, 2829, 2992, 3161, 3334, 3512, 3695, 3882, 4073, 4270, 4471, 4676, 4886, 5101, 5320, 5544, 5773

Offset: 0

Author

A. Timothy Royappa, Jun 17 2024

Keywords

• nonn
• easy

Comments

Maximum number of equilateral triangles with unit side, possibly cut into pieces, that can fit into a square of side n without overlapping.

The area of an equilateral triangle with unit side is sqrt(3)/4 (A120011), which gives the number a(n) of such triangles in a square of side n as at most floor(n^2/(sqrt(3)/4)).

Examples

			At most 9 unit equilateral triangles can fit into a square of side 2, so a(2) = 9.
		

Crossrefs

Cf. A120011.

Formula

a(n) = floor(4*n^2/sqrt(3)).