%I #46 Apr 16 2023 09:22:33
%S 1,2,3,9,21,68,208,730,2542,9287,34053,127112,476849,1803636,6851960,
%T 26157362,100211446,385239872,1485232325,5741327939,22246061118,
%U 86383655207,336093789246,1309999171971,5114453234510,19998176771431,78306018629550,307022197845116
%N Rectangular free polyominoes: number of n-celled polyominoes when the cell is a rectangle.
%H John Mason, <a href="/A056780/b056780.txt">Table of n, a(n) for n = 1..50</a>
%H R. J. Mathar, <a href="/A056780/a056780.pdf">Illustration of shapes up to 7-ominoes</a>
%H Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>
%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/minio/images/s1.gif">The 21 5-celled rectangular polyominoes</a>
%H M. Vicher, <a href="/A056780/a056780.gif">The 21 5-celled rectangular polyominoes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyrect.html">Polyrect</a> [From _Eric W. Weisstein_, Apr 24 2009]
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%F a(n) = 2*A006749(n) + 2*A006746(n) + A006748(n) + 2*A006747(n) + 2*A056877(n) + A056878(n) + A144553(n) + A142886(n). - _Andrew Howroyd_, Dec 04 2018
%t A[s_] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[Import[ "https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _} ][[All, 2]]];
%t A006749 = A@006749; A006746 = A@006746; A006748 = A@006748;
%t A006747 = A@006747; A056877 = A@056877; A056878 = A@056878;
%t A144553 = A@144553; A142886 = A@142886;
%t a[n_] := 2*A006749[[n]] + 2*A006746[[n]] + A006748[[n]] + 2*A006747[[n]] + 2*A056877[[n]] + A056878[[n]] + A144553[[n]] + A142886[[n + 1]];
%t Array[a, 28] (* _Jean-François Alcover_, Mar 26 2020 *)
%Y Cf. A000105 (cell is square), A151522 (1-sided), A001168 (fixed).
%K nice,nonn,hard
%O 1,2
%A _James A. Sellers_, Aug 28 2000
%E Edited by _N. J. A. Sloane_, Apr 25, 2001
%E Two more terms from _Ed Pegg Jr_, May 13 2009
%E a(13)-a(18) from _Joseph Myers_, Nov 15 2010
%E a(19)-a(28) from _Andrew Howroyd_, Dec 04 2018