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 A357197 #14 Sep 18 2022 12:37:34 %S A357197 6,12,30,60,102,156,222,300,390,468,606,708,870,1020,1152,1356,1542, %T A357197 1740,1950,2112,2406,2652,2910,3072,3462,3756,4062,4350,4710,4974, %U A357197 5406,5772,6126,6540,6918,7260,7782,8220,8646,8946,9606,10032,10590,11052,11568,12156,12702,13116,13830,14388 %N A357197 Number of vertices in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts. %C A357197 Unlike similar dissections of the triangle and square, see A357007 and A357060, there is no obvious pattern for n values that yield hexagons with non-simple intersections; these n values begin 9, 11, 14, 19, 23, 27, 29, 32, 34, 35, 38, 39, 41, 43, ... . %H A357197 Scott R. Shannon, <a href="/A357197/a357197.png">Image for n = 1</a>. %H A357197 Scott R. Shannon, <a href="/A357197/a357197_1.png">Image for n = 2</a>. %H A357197 Scott R. Shannon, <a href="/A357197/a357197_2.png">Image for n = 5</a>. %H A357197 Scott R. Shannon, <a href="/A357197/a357197_3.png">Image for n = 9</a>. This is the first term that forms hexagons with non-simple intersections. %H A357197 Scott R. Shannon, <a href="/A357197/a357197_4.png">Image for n = 50</a>. %H A357197 Scott R. Shannon, <a href="/A357197/a357197_5.png">Image for n = 150</a>. %F A357197 a(n) = A357198(n) - A357196(n) + 1 by Euler's formula. %F A357197 Conjecture: a(n) = 6*n^2 + 6 for hexagons that only contain simple intersections when cut by n internal hexagons. %Y A357197 Cf. A357196 (regions), A357198 (edges), A330846, A357007 (triangle), A357060 (square). %K A357197 nonn %O A357197 0,1 %A A357197 _Scott R. Shannon_, Sep 17 2022