cp's OEIS Frontend

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

%I A348010 #12 Sep 26 2021 13:07:20
%S A348010 1,2,6,14,40,96,268,664,1820,4588,12464,31712,85704,219376,590640,
%T A348010 1518652,4077112,10518364,28177388,72883016,194910964,505202708,
%U A348010 1349189968,3503014492,9344407884,24296044256,64748290040,168550939272
%N A348010 Number of n-step self-avoiding walks on the upper half-plane of a 2D square lattice rotated by Pi/4.
%H A348010 A. J. Guttmann and G. M. Torrie, <a href="https://doi.org/10.1088/0305-4470/17/18/023">Critical behavior at an edge for the SAW and Ising model</a>, J. Phys. A 17 (1984), 3539-3552.
%e A348010 The rotated lattice, where * is the origin and + are the lattice points, is:
%e A348010       +       +       +       +
%e A348010         \   /   \   /   \   /
%e A348010           +       +       +
%e A348010         /   \   /   \   /   \
%e A348010       +       +       +       +
%e A348010         \   /   \   /   \   /
%e A348010      -----+-------*-------+------
%e A348010 .
%e A348010 a(1) = 2 as the only two steps available are the diagonal steps to the northeast and northwest of the origin.
%e A348010 a(2) = 6 as from each of the available first steps three steps are possible, giving a total of 2 * 3 = 6 steps.
%Y A348010 Cf. A116903 (not rotated), A001411.
%K A348010 nonn,walk
%O A348010 0,2
%A A348010 _Scott R. Shannon_, Sep 24 2021