A335628 - OEIS

A335628

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

1, 2, 3, 6, 11, 20, 37, 68, 123, 232, 457, 879, 1679, 3269, 6478, 12799, 25272, 50127, 99888, 198867, 396267, 791069, 1580460, 3156095, 6305694, 12606152, 25205005, 50388077

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OFFSET

0,2

COMMENTS

This is a variation of A328078 and A334630 where the square is dissected with both orthogonal and diagonal lines.

For the first generation, a single orthogonal dissection line is drawn from the bottom to the top edge of the square. For the second generation, a single diagonal line is drawn from the bottom left corner toward to top right corner. The edge where the dissections start now rotates clockwise around the square and the dissection size halves. For the third generation, two orthogonal dissection lines are drawn from the left edge toward the right edge. For the fourth generation, four diagonal lines, two from the left edge and two from the top edge, are drawn from the top-left corner toward the bottom right corner. The edge now rotates clockwise again and the dissection size halves. The sequences gives the number of regions in the resulting dissection after generation n.

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

LINKS

Table of n, a(n) for n=0..27.

Scott R. Shannon, Illustration for n=2.

Scott R. Shannon, Illustration for n=3.

Scott R. Shannon, Illustration for n=4.

Scott R. Shannon, Illustration for n=5.

Scott R. Shannon, Illustration for n=6.

Scott R. Shannon, Illustration for n=7.

Scott R. Shannon, Illustration for n=8.

Scott R. Shannon, Illustration for n=9.

Scott R. Shannon, Illustration for n=10.