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Number of n-step self-avoiding walks starting at the origin that are restricted to the boundary walls of the first octant of the cubic lattice.
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%I #33 Oct 28 2023 09:23:50

%S 1,3,9,27,75,213,585,1623,4425,12123,32883,89415,241557,653649,

%T 1760427,4747005,12754593,34301463,91990575,246880023,661075149,

%U 1771199169,4736741853,12673587057,33856816431,90482953989,241499070195,644781165933,1719559634451,4587222964881,12225165127887

%N Number of n-step self-avoiding walks starting at the origin that are restricted to the boundary walls of the first octant of the cubic lattice.

%C These are walks in the first octant of the cubic lattice, never leaving the three walls forming the octant. The walls are the sets of points (x>=0, y>=0, z=0), (x>=0, y=0, z>=0), and (x=0, y>=0, z>=0) with (x,y,z) in Z^3.

%H Francois Alcover, <a href="/A330079/a330079.png">14-step walk</a>

%H Francois Alcover, <a href="/A330079/a330079.js.txt">nodejs script</a>

%Y Cf. A001411, A001412.

%Y The "snake in the box" problem (A000937, A099155) has a similar flavor. - _N. J. A. Sloane_, Dec 01 2019

%K nonn,walk

%O 0,2

%A _Francois Alcover_, Nov 30 2019

%E a(18)-a(25) _Scott R. Shannon_, Aug 17 2020

%E a(26)-a(30) from _Bert Dobbelaere_, Oct 28 2023