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Number of strictly 2-dimensional polyominoes with n cells.
(Formerly M3421)
5

%I M3421 #46 Apr 15 2023 12:27:23

%S 0,0,1,4,11,34,107,368,1284,4654,17072,63599,238590,901970,3426575,

%T 13079254,50107908,192622051,742624231,2870671949,11123060677,

%U 43191857687,168047007727,654999700402,2557227044763,9999088822074,39153010938486,153511100594602,602621953061977,2368347037571251,9317706529987949,36695016991712878

%N Number of strictly 2-dimensional polyominoes with n cells.

%C A000105 is the main entry for this sequence.

%D Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H John Mason, <a href="/A006765/b006765.txt">Table of n, a(n) for n = 1..50</a> (terms 1..45 from N. J. A. Sloane)

%H W. F. Lunnon, <a href="http://dx.doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>. Computer Journal 18 (1975), no. 4, pp. 366-367.

%H R. C. Schroeppel, <a href="http://www.experimentalmath.info/workshop2004/schroeppel-talk.pdf">A few mathematical experiments</a>, Experimental Mathematics Workshop, Oakland, California, March 30, 2004.

%t Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]] - 1 // Rest (* _Jean-François Alcover_, Jan 21 2020 *)

%Y Equals A000105(n)-1. A row of A049429. A column of A049430.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E Edited by _N. J. A. Sloane_, Sep 23 2011

%E Name clarified by _John Mason_, Jan 10 2023