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A330079
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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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1
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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
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..25.
Francois Alcover, 14-step walk
Francois Alcover, nodejs script
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CROSSREFS
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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
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KEYWORD
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nonn,more,walk
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AUTHOR
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Francois Alcover, Nov 30 2019
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EXTENSIONS
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a(18)-a(25) Scott R. Shannon, Aug 17 2020
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STATUS
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approved
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