cp's OEIS Frontend

A006744 Number of n-step self-avoiding walks on a Manhattan lattice.

%I A006744 M1073 #37 Feb 18 2020 03:40:11
%S A006744 1,2,4,7,13,24,44,77,139,250,450,788,1403,2498,4447,7782,13769,24363,
%T A006744 43106,75396,132865,234171,412731,721433,1267901,2228666,3917654,
%U A006744 6843596,12004150,21059478,36947904,64506130,112983428,197921386,346735329,605046571,1058544744,1852200487
%N A006744 Number of n-step self-avoiding walks on a Manhattan lattice.
%C A006744 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 A006744 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006744 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 A006744 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 A006744 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 A006744 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 A006744 Cf. A117633.
%K A006744 nonn,walk
%O A006744 1,2
%A A006744 _Simon Plouffe_