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

1, 2, 4, 7, 13, 24, 44, 77, 139, 250, 450, 788, 1403, 2498, 4447, 7782, 13769, 24363, 43106, 75396, 132865, 234171, 412731, 721433, 1267901, 2228666, 3917654, 6843596, 12004150, 21059478, 36947904, 64506130, 112983428, 197921386, 346735329, 605046571, 1058544744, 1852200487

Offset: 1

Author

Simon Plouffe

Keywords

• nonn
• walk

Comments

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

References

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

Links

• H. Jamke, Table of n, a(n) for n=1..53 [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 13 2010]
• D. Bennett-Wood, J. L. Cardy, I. Enting, A. J. Guttmann and A. L. Owczarek, On the Non-Universality of a Critical Exponent for Self-Avoiding Walks, Nuc. Phys. B, 528, 533-552, 1998. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 13 2010] Also wayback, or arxiv:9805146.
• A. Malakis, Self-avoiding walks on oriented square lattices, J. Phys. A: Math. Gen. 8 (1975), no 12, 1885-1898.
• S. S. Manna and A. J. Guttmann, Kinetic growth walks and trails on oriented square lattices: Hull percolation and percolation hulls, J. Phys. A 22 (1989), 3113-3122.

Crossrefs

Cf. A117633.