A348010 Number of n-step self-avoiding walks on the upper half-plane of a 2D square lattice rotated by Pi/4.

1, 2, 6, 14, 40, 96, 268, 664, 1820, 4588, 12464, 31712, 85704, 219376, 590640, 1518652, 4077112, 10518364, 28177388, 72883016, 194910964, 505202708, 1349189968, 3503014492, 9344407884, 24296044256, 64748290040, 168550939272

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. J. Guttmann and G. M. Torrie, Critical behavior at an edge for the SAW and Ising model, J. Phys. A 17 (1984), 3539-3552.

Example

The rotated lattice, where * is the origin and + are the lattice points, is:
      +       +       +       +
        \   /   \   /   \   /
          +       +       +
        /   \   /   \   /   \
      +       +       +       +
        \   /   \   /   \   /
     -----+-------*-------+------
.
a(1) = 2 as the only two steps available are the diagonal steps to the northeast and northwest of the origin.
a(2) = 6 as from each of the available first steps three steps are possible, giving a total of 2 * 3 = 6 steps.

Crossrefs

Cf. A116903 (not rotated), A001411.

Sequence in context: A263731 A293742 A299119 * A271895 A151538 A284998

Adjacent sequences: A348007 A348008 A348009 * A348011 A348012 A348013

Keyword

nonn,walk

Author

Scott R. Shannon, Sep 24 2021

Status

approved