Search: id:A000162
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%I A000162 M1845 N0731
%S A000162 1,1,2,8,29,166,1023,6922,48311,346543,2522522,18598427,138462649,
%T A000162 1039496297,7859514470,59795121480
%N A000162 Number of 3-dimensional polyominoes (or polycubes) with n cells.
%D A000162 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000162 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000162 C. J. Bouwkamp, personal communication.
%D A000162 D. A. Klarner, Some results concerning polyominoes, Fib. Quart., 3 (1965), 
               9-20.
%D A000162 J. R. Long and R. H. Holm, Enumeration and structural classification 
               of clusters derived from parent solids ..., J. Amer. Chem. Soc., 
               116 (1984), 9987-10002.
%D A000162 W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 
               of R. C. Read, editor, Graph Theory and Computing. Academic Press, 
               NY, 1972.
%D A000162 W. F. Lunnon, personal communication.
%H A000162 A. Clarke, <a href="http://www.geocities.com/alclarke0">Polyiamonds</
               a>
%H A000162 A. Clarke, <a href="a162.gif">The 8 tetracubes.</a>
%H A000162 M. Keller, <a href="http://www.solitairelaboratory.com/polyenum.html">
               Counting polyforms</a>
%H A000162 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Polycube.html">Link to a section of The World of Mathematics.</a>
%H A000162 Kevin L. Gong, <a href="http://kevingong.com/Polyominoes/Enumeration.html">
               Polyominoes Home Page.</a>
%e A000162 Table showing total number and numbers with each group order.
%e A000162 -------------------------------------------------------------
%e A000162 The last 7 columns form sequences A066453, A066454, A066273, A066281, 
               A066283, A066287, A066288.
%e A000162 .n ...A000162 ..group:.1.....2...3...4.6.8.24
%e A000162 .1 .........1..........0.....0...0...0.0.0..1
%e A000162 .2 .........1..........0.....0...0...0.0.1..0
%e A000162 .3 .........2..........0.....1...0...0.0.1..0
%e A000162 .4 .........8..........1.....4...1...0.0.2..0
%e A000162 .5 ........29.........17....10...0...0.0.2..0
%e A000162 .6 .......166........127....34...0...3.1.1..0
%e A000162 .7 ......1023........941....71...4...5.0.1..1
%e A000162 .8 ......6922.......6662...246...0..11.0.2..1
%e A000162 .9 .....48311......47771...522...3..11.0.4..0
%e A000162 10 ....346543.....344708..1783..24..24.2.2..0
%e A000162 11 ...2522522....2518713..3765...4..35.0.5..0
%e A000162 12 ..18598427...18585455.12858..18..84.5.7..0
%e A000162 13 .138462649..138434899.27496.151..92.2.8..1
%e A000162 14 1039496297.1039401564.94525..25.174.4.5..0
%Y A000162 A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - a(n), a(n) = 2*A038119 
               - A007743.
%Y A000162 a(n) = A066453 + A066545 + A066273 + A066281 + A066283 + A066287 + A066288.
%Y A000162 Cf. A038119, A007743, A066453.
%Y A000162 Sequence in context: A150757 A150758 A009419 this_sequence A052437 A131318 
               A010749
%Y A000162 Adjacent sequences: A000159 A000160 A000161 this_sequence A000163 A000164 
               A000165
%K A000162 nonn,nice,hard
%O A000162 1,3
%A A000162 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
%E A000162 The old value for a(11), 2522572, was corrected by Achim Flammenkamp 
               (achim(AT)uni-bielefeld.de) to 2522522, Feb 15 1999.
%E A000162 a(13) and a(14) from Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27, 
               2001
%E A000162 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007

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