cp's OEIS Frontend

A337675 Number of regions after generation n of Conant's dissection of a square where the starting edge rotates clockwise around the square and the dissection halves in size after every generation.

%I A337675 #13 Sep 16 2020 02:25:57
%S A337675 1,2,4,10,30,78,302,1038,4174,14670,60238,237902,955726,3704142,
%T A337675 14935374,60015950,239994190,951256398
%N A337675 Number of regions after generation n of Conant's dissection of a square where the starting edge rotates clockwise around the square and the dissection halves in size after every generation.
%C A337675 This is a variation of A335703 where the edge where the dissections begin starts at the bottom edge of the square and then proceeds clockwise around the square after each generation. However unlike A335703, where the dissection halves in size after every two generations, here it halves in size after every single generation. The resulting pattern, which resembles images of a printed circuit for large n, stays fairly constant while the internal regions are cut into smaller rectangles and squares after each generation.
%C A337675 The author thanks Rémy Sigrist whose code given in A328078 was modified to generate the larger values of this sequence.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675.png">Illustration for n=2</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_1.png">Illustration for n=3</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_2.png">Illustration for n=4</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_3.png">Illustration for n=5</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_4.png">Illustration for n=6</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_5.png">Illustration for n=7</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_6.png">Illustration for n=8</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_7.png">Illustration for n=9</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_8.png">Illustration for n=10</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_9.png">Illustration for n=11</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_10.png">Illustration for n=12</a>.
%H A337675 Scott R. Shannon, <a href="/A337675/a337675_11.png">Illustration for n=13</a>.
%Y A337675 Cf. A335703, A328078, A337270, A334630, A335093.
%K A337675 nonn,more
%O A337675 0,2
%A A337675 _Scott R. Shannon_, Sep 15 2020