A056780 Rectangular free polyominoes: number of n-celled polyominoes when the cell is a rectangle.

1, 2, 3, 9, 21, 68, 208, 730, 2542, 9287, 34053, 127112, 476849, 1803636, 6851960, 26157362, 100211446, 385239872, 1485232325, 5741327939, 22246061118, 86383655207, 336093789246, 1309999171971, 5114453234510, 19998176771431, 78306018629550, 307022197845116

Offset: 1

Author

James Sellers, Aug 28 2000

Keywords

• nice
• nonn
• hard

Links

• John Mason, Table of n, a(n) for n = 1..50
• R. J. Mathar, Illustration of shapes up to 7-ominoes
• Ed Pegg, Jr., Illustrations of polyforms
• M. Vicher, Polyforms
• M. Vicher, The 21 5-celled rectangular polyominoes
• M. Vicher, The 21 5-celled rectangular polyominoes
• Eric Weisstein's World of Mathematics, Polyrect [From _Eric W. Weisstein_, Apr 24 2009]
• Wikipedia, Polyomino

Crossrefs

Cf. A000105 (cell is square), A151522 (1-sided), A001168 (fixed).

Programs

Mathematica

A[s_] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[Import[ "https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, } ][[All, 2]]];
A006749 = A@006749; A006746 = A@006746; A006748 = A@006748;
A006747 = A@006747; A056877 = A@056877; A056878 = A@056878;
A144553 = A@144553; A142886 = A@142886;
a[n_] := 2*A006749[[n]] + 2*A006746[[n]] + A006748[[n]] + 2*A006747[[n]] + 2*A056877[[n]] + A056878[[n]] + A144553[[n]] + A142886[[n + 1]];
Array[a, 28] (* Jean-François Alcover, Mar 26 2020 *)

Formula

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

Extensions

Edited by N. J. A. Sloane, Apr 25 2001

Two more terms from Ed Pegg Jr, May 13 2009

a(13)-a(18) from Joseph Myers, Nov 15 2010

a(19)-a(28) from Andrew Howroyd, Dec 04 2018