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 A298267 #33 Jan 22 2018 19:27:09 %S A298267 0,3,7,13,21,30,42,54,69,85,103,123,144,168,192,219,247,277,309,342, %T A298267 378,414,453,493,535,579,624,672,720,771,823,877,933,990,1050,1110, %U A298267 1173,1237,1303,1371,1440,1512,1584,1659,1735,1813,1893,1974,2058,2142 %N A298267 a(n) is the maximum number of heptiamonds in a hexagon of order n. %C A298267 There are 24 heptiamonds. %C A298267 It would be nice if this idea could be generalized to state that the hexagon can contain the maximum number of polyiamonds of any given size. %H A298267 Michael De Vlieger, <a href="/A298267/b298267.txt">Table of n, a(n) for n = 0..10000</a> %H A298267 Craig Knecht, <a href="/A298267/a298267.png">H2 Hexagon with 3 heptiamonds packed in.</a> %H A298267 Craig Knecht, <a href="/A298267/a298267_1.png">H3 hexagon with 7 heptiamonds packed in.</a> %H A298267 Craig Knecht, <a href="/A298267/a298267_2.png">H4 H5 H6 H7 heptiamond packing.</a> %H A298267 Craig Knecht, <a href="/A298267/a298267_6.png">Peripheral Buildouts.</a> %H A298267 Craig Knecht, <a href="/A298267/a298267_8.png">Proof notes.</a> %F A298267 a(n) = floor((6*n^2)/7). %F A298267 Conjectures from _Colin Barker_, Jan 20 2018: (Start) %F A298267 G.f.: x*(1 + x)*(3 - 2*x + 4*x^2 - 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). %F A298267 a(n) = 2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9) for n>8. %F A298267 (End) %t A298267 Array[Floor[(6 #^2)/7] &, 50] (* _Michael De Vlieger_, Jan 20 2018 *) %Y A298267 Cf. A033581 (The number of triangles in a hexagon), A291582 (hexiamond tiling). %K A298267 nonn %O A298267 0,2 %A A298267 _Craig Knecht_, Jan 15 2018