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A000162 Number of 3-dimensional polyominoes (or polycubes) with n cells.
(Formerly M1845 N0731)
33

%I M1845 N0731

%S 1,1,2,8,29,166,1023,6922,48311,346543,2522522,18598427,138462649,

%T 1039496297,7859514470,59795121480

%N Number of 3-dimensional polyominoes (or polycubes) with n cells.

%D C. J. Bouwkamp, personal communication.

%D 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 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 W. F. Lunnon, personal communication.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H C. J. Bouwkamp & N. J. A. Sloane, <a href="/A000162/a000162.pdf">Correspondence, 1971</a>

%H A. Clarke, <a href="http://www.recmath.com/PolyPages/PolyPages/Polycubes.html">Polycubes</a>

%H A. Clarke, <a href="/A000162/a000162.gif">The 8 tetracubes.</a>

%H Kevin L. Gong, <a href="http://kevingong.com/Polyominoes/Enumeration.html">Polyominoes Home Page.</a>

%H M. Keller, <a href="http://www.solitairelaboratory.com/polyenum.html">Counting polyforms</a>

%H David A. Klarner, <a href="http://www.fq.math.ca/Scanned/3-1/klarner.pdf">Some results concerning polyominoes</a>, Fibonacci Quarterly 3 (1965), 9-20.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polycube.html">Polycube</a>

%F a(n) = A066273 + A066281 + A066283 + A066287 + A066288 + A066453 + A066545.

%F a(n) = 2*A038119 - A007743.

%F a(n) = A000105 + A006759.

%e Table showing total number and numbers with each group order.

%e -------------------------------------------------------------

%e The last 7 columns form sequences A066453, A066454, A066273, A066281, A066283, A066287, A066288.

%e .n ...A000162 ..group:.1.....2...3...4.6.8.24

%e .1 .........1..........0.....0...0...0.0.0..1

%e .2 .........1..........0.....0...0...0.0.1..0

%e .3 .........2..........0.....1...0...0.0.1..0

%e .4 .........8..........1.....4...1...0.0.2..0

%e .5 ........29.........17....10...0...0.0.2..0

%e .6 .......166........127....34...0...3.1.1..0

%e .7 ......1023........941....71...4...5.0.1..1

%e .8 ......6922.......6662...246...0..11.0.2..1

%e .9 .....48311......47771...522...3..11.0.4..0

%e 10 ....346543.....344708..1783..24..24.2.2..0

%e 11 ...2522522....2518713..3765...4..35.0.5..0

%e 12 ..18598427...18585455.12858..18..84.5.7..0

%e 13 .138462649..138434899.27496.151..92.2.8..1

%e 14 1039496297.1039401564.94525..25.174.4.5..0

%Y Cf. A001931, A038119, A007743, A066453.

%K nonn,nice,hard,more

%O 1,3

%A _N. J. A. Sloane_ and _J. H. Conway_

%E The old value for a(11), 2522572, was corrected by _Achim Flammenkamp_ to 2522522, Feb 15 1999.

%E a(13) and a(14) from Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27, 2001

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007

%E Link updated by _William Rex Marshall_, Dec 16 2009

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)