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Number of "polyares" of order n (turning over allowed).
2

%I #24 Mar 19 2023 08:22:05

%S 1,3,9,42,180,889,4392,22432,115469,602112,3161949,16723643,88933764,

%T 475286752,2550780323

%N Number of "polyares" of order n (turning over allowed).

%C An n-are is a shape formed from an n-celled polyomino by removing half of each cell such that edge connections are not broken.

%D Enumeration attributed by Andrew Clarke to Brendan Owen.

%H Andrew Clarke, <a href="http://www.recmath.com/PolyPages/PolyPages/Polyares.htm">Polyares</a>

%H Andrew Clarke, <a href="/A057724/a057724.gif">Picture from Andrew Clarke's page showing the 9 polyares of order 3 when turning over is allowed.</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a057/A057724.java">Java program</a> (github)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyare.html">Polyare</a>

%Y Cf. A057725, A000105.

%K nonn,nice,more

%O 1,2

%A _N. J. A. Sloane_, Oct 29 2000

%E Link updated by _William Rex Marshall_, Dec 16 2009

%E a(9)-a(11) from _Sean A. Irvine_, Jul 02 2022

%E Corrected a(8) and added a(12)-a(15) by _John Mason_, Mar 19 2023