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 A335093 #21 Feb 22 2021 20:13:47 %S A335093 1,2,3,5,7,12,18,33,57,105,186,348,648,1226,2347,4535,8840,17386, %T A335093 34229,67708,134210,266779,531277,1058724,2112238,4215738,8421830, %U A335093 16822772,33624420,67204921,134363536,268636845,537171420,1074115099 %N A335093 Number of regions after generation n of Conant's dissection of a square when dissected with diagonal lines and where the starting pair of edges rotates counterclockwise around the square. %C A335093 This is a variation of A334630 where the pair of edges where the dissection begins starts at the left and bottom edges of the square and then proceeds counterclockwise around the square, the dissection halving in size after every two steps. %C A335093 For the first generation a single dissection line is drawn from the bottom left to the top right corner of the square. For the second generation a single line is drawn from the bottom right corner toward to top left corner. For the third generation the dissection size halves and moves counterclockwise so now two lines are drawn from the top edge toward the left edge and also two lines from the right edge toward the bottom edge. For the fourth generation two lines are drawn from the top edge toward the right edge and two lines from the left edge toward the bottom edge. The dissection again moves counterclockwise and halves in size so now starts at the left and bottom edge again, and for the fifth generation draws four lines on each edge. The sequence gives the number of regions in the resulting dissection after generation n. %C A335093 Like the standard orthogonal lines dissection of A328078 no obvious repetitive pattern appears as the generations increases. But unlike A334630 there appears to be no high density horizontal lines appearing in the resulting dissection, see the linked images. %C A335093 The author thanks _Rémy Sigrist_ whose code given in A328078 was modified to generate the larger values of this sequence. %H A335093 Scott R. Shannon, <a href="/A335093/a335093.png">Illustration for n=3</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_1.png">Illustration for n=4</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_2.png">Illustration for n=5</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_3.png">Illustration for n=6</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_4.png">Illustration for n=7</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_5.png">Illustration for n=8</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_6.png">Illustration for n=9</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_7.png">Illustration for n=10</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_8.png">Illustration for n=11</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_9.png">Illustration for n=12</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_10.png">Illustration for n=13</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_11.png">Illustration for n=14</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_12.png">Illustration for n=15</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_13.png">Illustration for n=16</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_14.png">Illustration for n=17</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_15.png">Illustration for n=18</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_16.png">Illustration for n=19</a>. %H A335093 Scott R. Shannon, <a href="/A335093/a335093_17.png">Illustration for n=20</a>. %Y A335093 Cf. A334630, A328078, A335703, A337270. %K A335093 nonn,more %O A335093 0,2 %A A335093 _Scott R. Shannon_, Sep 12 2020