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Search: id:A001168
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| A001168 |
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Number of fixed polyominoes with n cells. (Formerly M1639 N0641)
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+0 15
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| 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861, 1903890, 7204874, 27394666, 104592937, 400795844, 1540820542, 5940738676, 22964779660, 88983512783, 345532572678, 1344372335524, 5239988770268, 20457802016011, 79992676367108, 313224032098244, 1228088671826973
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen. 28(1995) 891-904.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 378-382.
J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 229.
I. Jensen and A. J. Guttmann, Statistics of lattice animals (polyominoes) and polygons. J. Phys. A 33, L257-L263 (2000).
W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.
W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87-100 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
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LINKS
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I. Jensen, Table of n, a(n) for n = 1..56
S. R. Finch, Klarner's Lattice Animal Constant
I. Jensen, Home page
I. Jensen, More terms
D. E. Knuth, Program
D. E. Knuth, First 47 terms
Tomas Oliveira e Silva, Enumeration of polyominoes
Eric Weisstein's World of Mathematics, Polyomino
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CROSSREFS
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Cf. A000105, A006746, A056877, A006748, A056878, A006747, A006749, A006884, A006885, A006877, A006878, A033492.
A006762 is another version.
Sequence in context: A006724 A057409 A001170 this_sequence A119255 A071969 A063030
Adjacent sequences: A001165 A001166 A001167 this_sequence A001169 A001170 A001171
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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Extended to n=28 by Tomas Oliveira e Silva. Extended to n=46 by Iwan Jensen. Verified (and one more term found) by D. E. Knuth, Jan 09 2001.
Richard Schroeppel communicated Jensen's calculation of the first 56 terms, Feb 21 2005
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