

A330079


Number of nstep selfavoiding walks starting at the origin that are restricted to the boundary walls of the first octant of the cubic lattice.


1



1, 3, 9, 27, 75, 213, 585, 1623, 4425, 12123, 32883, 89415, 241557, 653649, 1760427, 4747005, 12754593, 34301463, 91990575, 246880023, 661075149, 1771199169, 4736741853, 12673587057, 33856816431, 90482953989
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OFFSET

0,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..25.
Francois Alcover, 14step walk
Francois Alcover, nodejs script


CROSSREFS

Cf. A001411, A001412.
The "snake in the box" problem (A000937, A099155) has a similar flavor.  N. J. A. Sloane, Dec 01 2019
Sequence in context: A180238 A289693 A269684 * A135415 A182897 A228734
Adjacent sequences: A330076 A330077 A330078 * A330080 A330081 A330082


KEYWORD

nonn,more,walk


AUTHOR

Francois Alcover, Nov 30 2019


EXTENSIONS

a(18)a(25) Scott R. Shannon, Aug 17 2020


STATUS

approved



