A057787 Number of polyarcs with n cells.

2, 7, 22, 93, 364, 1734, 8246, 41043, 206602, 1056831, 5454954, 28394727, 148805868, 784390909

Offset: 1

Author

N. J. A. Sloane, Nov 04 2000

Keywords

• nonn
• nice
• more

Comments

Draw a quarter circle with radius one, centered at the corner of a unit square. It divides the square into two pieces. Call these pieces monarcs. Polyarcs are the figures created by joining monarcs edge-to-edge. - Henri Picciotto, Jan 04 2015

Henri Picciotto invented and named the polyarcs in the late 1980’s. They were first published in World Games Review, Michael Keller’s zine. Brendan Owen found and counted the polyarcs to n = 9. - N. J. A. Sloane, Mar 29 2015

When a complete square is present, the internal details of the division (which can happen in four ways) are ignored for the purposes of this sequence. - Sean A. Irvine, Jul 04 2022

Links

• Michael Keller, Diarcs and Triarcs, World Games Review 'Zine (#9, Dec 1989). [Illustration of a(3)=22]
• Michael Keller, Diarcs and Triarcs [Illustration of a(3)=22] [Cached copy in pdf format]
• Brendan Owen, Tetrarcs and Pentarcs [Illustration of a(4)=93, a(5)=364]
• Brendan Owen, Tetrarcs and Pentarcs [Illustration of a(4)=93, a(5)=364] [Cached copy in pdf format]
• Henri Picciotto's Math Education Page, Polyarcs, in Geometric Puzzles in the Classroom. Also contains other polyarc links.
• Henri Picciotto, Illustration of definition, a(1)=2 and a(2)=7. [A brief section from Geometric Puzzles in the Classroom]

Extensions

a(10)-a(14) from Aaron N. Siegel, May 12 2022