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

0,2

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..30.

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

Sequence in context: A180238 A289693 A269684 * A361423 A135415 A182897

Adjacent sequences: A330076 A330077 A330078 * A330080 A330081 A330082

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