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A330079
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.
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, 241499070195, 644781165933, 1719559634451, 4587222964881, 12225165127887
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
Francois Alcover, 14-step walk
Francois Alcover, nodejs script
CROSSREFS
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 * A361423 A135415 A182897
KEYWORD
nonn,walk
AUTHOR
Francois Alcover, Nov 30 2019
EXTENSIONS
a(18)-a(25) Scott R. Shannon, Aug 17 2020
a(26)-a(30) from Bert Dobbelaere, Oct 28 2023
STATUS
approved