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Search: id:A001394
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| A001394 |
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Number of n-step self-avoiding walks on diamond.
(Formerly M3452 N1403)
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+0
1
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| 1, 4, 12, 36, 108, 324, 948, 2796, 8196, 24060, 70188, 205284, 597996, 1744548, 5073900, 14774652, 42922452, 124814484, 362267652, 1052271732, 3051900516
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of 2 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004
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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).
J. W. Essam and M. F. Sykes, The crystal statistics of the diamond lattice, Physica, 29 (1963), 378-388.
A. J. Guttmann, On the critical behavior of self-avoiding walks II, J. Phys. A 22 (1989), 2807-2813.
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LINKS
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S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
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CROSSREFS
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Cf. A097700.
Sequence in context: A156945 A006817 A003119 this_sequence A156946 A003946 A052156
Adjacent sequences: A001391 A001392 A001393 this_sequence A001395 A001396 A001397
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KEYWORD
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nonn,walk,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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