A337693 - OEIS

A337693

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

%I #18 Feb 22 2021 20:13:28

%S 1,2,4,9,25,61,197,597,2165,7861,30549,118869,471765,1873621,7479637,

%T 29864277,119397205

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

%C This is a variation of A335093 in which the edges where the diagonal dissections begin start at the left and bottom edge of the square and then proceeds counterclockwise around the square after each generation. However unlike A335093, where the dissection halves in size after every two generations, here it halves in size after every single generation. The resulting pattern for larger n shows vertical and horizontal lines of higher density crossings similar to those seen in A334630.

%C The author thanks Rémy Sigrist whose code given in A328078 was modified to generate the larger values of this sequence.

%H Scott R. Shannon, <a href="/A337693/a337693.png">Illustration for n=2</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_1.png">Illustration for n=3</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_2.png">Illustration for n=4</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_3.png">Illustration for n=5</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_4.png">Illustration for n=6</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_5.png">Illustration for n=7</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_6.png">Illustration for n=8</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_7.png">Illustration for n=9</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_8.png">Illustration for n=10</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_9.png">Illustration for n=11</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_10.png">Illustration for n=12</a>.

%H Scott R. Shannon, <a href="/A337693/a337693_11.png">Illustration for n=13</a>.

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

%K nonn,more

%O 0,2

%A _Scott R. Shannon_, Sep 15 2020