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%I #23 Apr 16 2023 09:22:20
%S 1,2,4,13,35,120,392,1405,4998,18378,67792,253509,952534,3604624,
%T 13699554,52304807,200406370,770442286,2970401696,11482513428,
%U 44491881033,172766765654,672186650116,2619996250930,10228902882021,39996345469572,156612023354364,614044364443761
%N Number of 1-sided polyrhombs with n cells.
%C Also counts 1-sided polyrects.
%H John Mason, <a href="/A151522/b151522.txt">Table of n, a(n) for n = 1..50</a>
%H Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyrhomb.html">Polyrhomb</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyrect.html">Polyrect</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%F a(n) = 4*A006749(n) + 2*A006746(n) + 2*A006748(n) + 4*A006747(n) + 2*A056877(n) + 2*A056878(n) + 2*A144553(n) + A142886(n). - _Andrew Howroyd_, Dec 04 2018
%t A[n_] := With[{n6 = StringPadLeft[ToString[n], 6, "0"]}, Cases[ Import[ "https://oeis.org/A" <> n6 <> "/b" <> n6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A006749 = A@6749; A006746 = A@6746; A006748 = A@6748; A006747 = A@6747; A056877 = A@56877; A056878 = A@56878; A144553 = A@144553; A142886 = A@142886;
%t a[n_] := 4*A006749[[n]] + 2*A006746[[n]] + 2*A006748[[n]] + 4*A006747[[n]] + 2*A056877[[n]] + 2*A056878[[n]] + 2*A144553[[n]] + A142886[[n + 1]];
%t a /@ Range[28] (* _Jean-François Alcover_, Jan 03 2020 *)
%Y Polyominoes by group of symmetries relating shapes considered the same: A000105 (all symmetries), A001168 (translations only), A000988 (rotations and translations), A056780 (horizontal and vertical reflections, rotations of order 2 and translations), A056783 (reflections in either diagonal, rotations of order 2 and translations), A151522 (rotations of order 2 and translations), A151525 (reflections in a horizontal line and translations), A182645 (reflections in a NE-SW diagonal line and translations)
%K nonn,hard
%O 1,2
%A _Ed Pegg Jr_, May 13 2009
%E Edited and a(13)-a(18) by _Joseph Myers_, Nov 24 2010
%E a(19)-a(28) from _Andrew Howroyd_, Dec 04 2018
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