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Search: id:A000162
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| A000162 |
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Number of 3-dimensional polyominoes (or polycubes) with n cells.
(Formerly M1845 N0731)
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+0
21
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| 1, 1, 2, 8, 29, 166, 1023, 6922, 48311, 346543, 2522522, 18598427, 138462649, 1039496297, 7859514470, 59795121480
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
C. J. Bouwkamp, personal communication.
D. A. Klarner, Some results concerning polyominoes, Fib. Quart., 3 (1965), 9-20.
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.
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.
W. F. Lunnon, personal communication.
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LINKS
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A. Clarke, Polycubes
A. Clarke, The 8 tetracubes.
M. Keller, Counting polyforms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Kevin L. Gong, Polyominoes Home Page.
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EXAMPLE
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Table showing total number and numbers with each group order.
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The last 7 columns form sequences A066453, A066454, A066273, A066281, A066283, A066287, A066288.
.n ...A000162 ..group:.1.....2...3...4.6.8.24
.1 .........1..........0.....0...0...0.0.0..1
.2 .........1..........0.....0...0...0.0.1..0
.3 .........2..........0.....1...0...0.0.1..0
.4 .........8..........1.....4...1...0.0.2..0
.5 ........29.........17....10...0...0.0.2..0
.6 .......166........127....34...0...3.1.1..0
.7 ......1023........941....71...4...5.0.1..1
.8 ......6922.......6662...246...0..11.0.2..1
.9 .....48311......47771...522...3..11.0.4..0
10 ....346543.....344708..1783..24..24.2.2..0
11 ...2522522....2518713..3765...4..35.0.5..0
12 ..18598427...18585455.12858..18..84.5.7..0
13 .138462649..138434899.27496.151..92.2.8..1
14 1039496297.1039401564.94525..25.174.4.5..0
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CROSSREFS
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A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - a(n), a(n) = 2*A038119 - A007743.
a(n) = A066453 + A066545 + A066273 + A066281 + A066283 + A066287 + A066288.
Cf. A038119, A007743, A066453.
Sequence in context: A150757 A150758 A009419 this_sequence A052437 A131318 A010749
Adjacent sequences: A000159 A000160 A000161 this_sequence A000163 A000164 A000165
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KEYWORD
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nonn,nice,hard,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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The old value for a(11), 2522572, was corrected by Achim Flammenkamp (achim(AT)uni-bielefeld.de) to 2522522, Feb 15 1999.
a(13) and a(14) from Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27, 2001
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
Link updated by William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Dec 16 2009
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