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.

1, 2, 4, 10, 30, 78, 302, 1038, 4174, 14670, 60238, 237902, 955726, 3704142, 14935374, 60015950, 239994190, 951256398

Offset

0,2

Comments

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.

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..17.

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.

Scott R. Shannon, Illustration for n=11.

Scott R. Shannon, Illustration for n=12.

Scott R. Shannon, Illustration for n=13.

Crossrefs

Cf. A335703, A328078, A337270, A334630, A335093.

Sequence in context: A229905 A361791 A102667 * A148115 A361758 A148116

Adjacent sequences: A337672 A337673 A337674 * A337676 A337677 A337678

Keyword

nonn,more

Author

Scott R. Shannon, Sep 15 2020

Status

approved