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 A240439 #9 Apr 06 2014 03:27:06 %S A240439 1,1,1,3,3,1,6,15,15,3,1,10,45,105,114,39,3,1,15,105,420,969,1194,654, %T A240439 102,3,1,21,210,1260,4773,11259,15615,11412,3663,342,15,1,28,378,3150, %U A240439 17415,64776,159528,250233,234609,119259,28395,2613,69,1,36,630,6930 %N A240439 Triangle T(n, k) = Numbers of ways to place k points on a triangular grid of side n so that no three of them are vertices of an equilateral triangle of any orientation. Triangle read by rows. %C A240439 The triangle T(n, k) is irregularly shaped: 0 <= k <= A240114(n). First row corresponds to n = 1. %C A240439 The maximal number of points that can be placed on a triangular grid of side n so that no three of them form an equilateral triangle is given by A240114(n). %H A240439 Heinrich Ludwig, <a href="/A240439/b240439.txt">Table of n, a(n) for n = 1..138</a> %e A240439 The triangle begins: %e A240439 1, 1; %e A240439 1, 3, 3; %e A240439 1, 6, 15, 15, 3; %e A240439 1, 10, 45, 105, 114, 39, 3; %e A240439 1, 15, 105, 420, 969, 1194, 654, 102, 3; %e A240439 1, 21, 210, 1260, 4773, 11259, 15615, 11412, 3663, 342, 15; %e A240439 There are T(5, 8) = 3 ways to place 8 points (x) on a triangular grid of side 5 under the conditions mentioned above: %e A240439 . x x %e A240439 x x x . . x %e A240439 x . x x . . . . x %e A240439 x . . x x . . . . . . x %e A240439 x . . . x . x x x x x x x x . %Y A240439 Cf. A240114, A240443, A084546, %Y A240439 column 2 is A000217, %Y A240439 column 3 is A050534, %Y A240439 column 4 is A240440, %Y A240439 column 5 is A240441, %Y A240439 column 6 is A240442. %K A240439 nonn,tabf %O A240439 1,4 %A A240439 _Heinrich Ludwig_, Apr 05 2014