This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373732 #25 Jun 22 2024 14:14:45 %S A373732 0,2,9,20,36,57,83,113,147,187,230,279,332,390,452,519,591,667,748, %T A373732 833,923,1018,1117,1221,1330,1443,1561,1683,1810,1942,2078,2219,2364, %U A373732 2514,2669,2829,2992,3161,3334,3512,3695,3882,4073,4270,4471,4676,4886,5101,5320,5544,5773 %N A373732 a(n) = floor(4*n^2/sqrt(3)). %C A373732 Maximum number of equilateral triangles with unit side, possibly cut into pieces, that can fit into a square of side n without overlapping. %C A373732 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)). %F A373732 a(n) = floor(4*n^2/sqrt(3)). %e A373732 At most 9 unit equilateral triangles can fit into a square of side 2, so a(2) = 9. %Y A373732 Cf. A120011. %K A373732 nonn,easy %O A373732 0,2 %A A373732 _A. Timothy Royappa_, Jun 17 2024