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, 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

Author

Francois Alcover, Nov 30 2019

Keywords

• nonn
• walk

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

Cf. A001411, A001412.

The "snake in the box" problem (A000937, A099155) has a similar flavor. - N. J. A. Sloane, Dec 01 2019

Extensions

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

a(26)-a(30) from Bert Dobbelaere, Oct 28 2023