A335632 - OEIS

A335632

Number of regions after generation n of Conant's dissection of a square when dissected with both diagonal and orthogonal lines and where the starting edges rotate clockwise around the square and the dissection halves in size every second generation.

%I #13 Oct 07 2020 11:25:37

%S 1,2,3,8,11,25,37,97,142,316,463,1150,1747,4298,6599,16641,25800,

%T 65025,101027,256245,399972,1017939,1589375,4048559,6328766,16148228,

%U 25252615,53243252

%N Number of regions after generation n of Conant's dissection of a square when dissected with both diagonal and orthogonal lines and where the starting edges rotate clockwise around the square and the dissection halves in size every second generation.

%C This is a variation of A335628 where the same rules are applied but the first dissection is with a diagonal line from the lower left corner to the upper right corner, followed by dissection with an orthogonal line from the left edge. For further details see A335628.

%H Scott R. Shannon, <a href="/A335632/a335632.png">Illustration for n=2</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_1.png">Illustration for n=3</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_2.png">Illustration for n=4</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_3.png">Illustration for n=5</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_4.png">Illustration for n=6</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_5.png">Illustration for n=7</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_6.png">Illustration for n=8</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_7.png">Illustration for n=9</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_8.png">Illustration for n=10</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_9.png">Illustration for n=11</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_10.png">Illustration for n=12</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_11.png">Illustration for n=13</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_12.png">Illustration for n=14</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_13.png">Illustration for n=15</a>.

%H Scott R. Shannon, <a href="/A335632/a335632_14.png">Illustration for n=16</a>.

%Y Cf. A335628, A328078, A334630, A335703, A337270, A335093, A337675.

%K nonn,more

%O 0,2

%A _Scott R. Shannon_, Oct 03 2020