A056780 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

Eric Weisstein's World of Mathematics, Polyrect [From Eric W. Weisstein, Apr 24 2009]

Wikipedia, Polyomino

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

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 *)

CROSSREFS

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

Sequence in context: A099607 A077550 A301809 * A324614 A141505 A111360

Adjacent sequences: A056777 A056778 A056779 * A056781 A056782 A056783

KEYWORD

nice,nonn,hard

AUTHOR

James A. Sellers, Aug 28 2000

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

STATUS

approved