A354382 - OEIS

%I #8 May 25 2022 11:49:06

%S 2,32,700,21943,737164,25959013,938559884

%N Number of free pseudo-polyarcs with n cells.

%C See A057787 for a description of polyarcs. The pseudo-polyarcs are constructed in the same way as ordinary polyarcs, but allowing for corner-connections. Thus they generalize polyarcs in the same way that pseudo-polyominoes (aka polyplets, A030222) generalize ordinary polyominoes (A000105). They can also be viewed as the "rounded" variant of pseudo-polytans (A354380), in the same way that ordinary polyarcs are the rounded variant of ordinary polytans (A006074).

%C Two figures are considered equivalent if they differ only by a rotation or reflection.

%C The pseudo-polyarcs grow tremendously fast, much faster than most polyforms. The initial data that have been computed suggest an asymptotic growth rate of at least 36^n.

%H Aaron N. Siegel, <a href="/A354382/a354382.png">Illustration showing a(2) = 32</a>. The color of each figure corresponds to its number of symmetries.

%e a(10) = 32, because there are 32 ways of adjoining two monarcs: 7 distinct edge-to-edge joins, and 25 distinct corner-to-corner joins (including one double-corner join involving two concave arcs).

%Y Cf. A057787, A354380, A006074, A000105, A030222.

%K nonn,hard,more

%O 1,1

%A _Aaron N. Siegel_, May 24 2022