cp's OEIS Frontend

A057787 Number of polyarcs with n cells.

%I A057787 #42 Jul 04 2022 23:17:00
%S A057787 2,7,22,93,364,1734,8246,41043,206602,1056831,5454954,28394727,
%T A057787 148805868,784390909
%N A057787 Number of polyarcs with n cells.
%C A057787 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
%C A057787 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
%C A057787 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
%H A057787 Michael Keller, <a href="http://www.mathedpage.org/puzzles/polyarcs/polyarc-mk.html">Diarcs and Triarcs</a>, World Games Review 'Zine (#9, Dec 1989). [Illustration of a(3)=22]
%H A057787 Michael Keller, <a href="/A057787/a057787.pdf">Diarcs and Triarcs</a> [Illustration of a(3)=22] [Cached copy in pdf format]
%H A057787 Brendan Owen, <a href="http://www.picciotto.org/math-ed/puzzles/polyarcs/pentarcs-bo.html">Tetrarcs and Pentarcs</a> [Illustration of a(4)=93, a(5)=364]
%H A057787 Brendan Owen, <a href="/A057787/a057787_1.pdf">Tetrarcs and Pentarcs</a> [Illustration of a(4)=93, a(5)=364] [Cached copy in pdf format]
%H A057787 Henri Picciotto's Math Education Page, <a href="http://www.mathedpage.org/puzzles/#polyarcs">Polyarcs</a>, in Geometric Puzzles in the Classroom. Also contains other polyarc links.
%H A057787 Henri Picciotto, <a href="/A057787/a057787.png">Illustration of definition, a(1)=2 and a(2)=7.</a> [A brief section from Geometric Puzzles in the Classroom]
%K A057787 nonn,nice,more
%O A057787 1,1
%A A057787 _N. J. A. Sloane_, Nov 04 2000
%E A057787 a(10)-a(14) from _Aaron N. Siegel_, May 12 2022