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A006744 Number of n-step self-avoiding walks on a Manhattan lattice.
(Formerly M1073)
3

%I M1073

%S 1,2,4,7,13,24,44,77,139,250,450,788,1403,2498,4447,7782,13769,24363,

%T 43106,75396,132865,234171,412731,721433,1267901,2228666,3917654,

%U 6843596,12004150,21059478,36947904,64506130,112983428,197921386,346735329,605046571,1058544744,1852200487

%N Number of n-step self-avoiding walks on a Manhattan lattice.

%C It seems that a(n) = A117633(n)/2 (the two sequences have similar names). Sequence A117633 is based on the paper by Malakis (1975). - _Petros Hadjicostas_, Jan 02 2019

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

%H H. Jamke, <a href="/A006744/b006744.txt">Table of n, a(n) for n=1..53</a> [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 13 2010]

%H D. Bennett-Wood, J. L. Cardy, I. Enting, A. J. Guttmann and A. L. Owczarek, <a href="http://metis.ms.unimelb.edu.au/publications/pub-37-41.pdf">On the Non-Universality of a Critical Exponent for Self-Avoiding Walks</a>, Nuc. Phys. B, 528, 533-552, 1998. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 13 2010] Also <a href="http://web.archive.org/web/20060821115907id_/http://www.ms.unimelb.edu.au/publications/pub-37-41.pdf">wayback</a>, or <a href="https://arxiv.org/abs/cond-mat/9805146">arxiv:9805146</a>.

%H A. Malakis, <a href="https://doi.org/10.1088/0305-4470/8/12/007">Self-avoiding walks on oriented square lattices</a>, J. Phys. A: Math. Gen. 8 (1975), no 12, 1885-1898.

%H S. S. Manna and A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/22/15/025">Kinetic growth walks and trails on oriented square lattices: Hull percolation and percolation hulls</a>, J. Phys. A 22 (1989), 3113-3122.

%Y Cf. A117633.

%K nonn,walk

%O 1,2

%A _Simon Plouffe_

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)