A337021 The number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2x2x2 where the walk starts at the center of the box.

1, 6, 24, 72, 168, 456, 1032, 2712, 5784, 14640, 29760, 71136, 133344, 291696, 479232, 950880, 1343088, 2375808, 2774832, 4266240, 3909792, 5046672, 3230400, 3316704, 1122000, 808128, 0

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

For n>=27 all terms are 0 as the walk contains more steps than there are available lattice points in the 2x2x2 box.

Example

a(1) = 6 as the walk is free to move one step in all six axial directions.
a(2) = 24 as after a step in one of the six axial directions the walk must turn along the face of the box; this eliminates the 2-step straight walk in all directions, so the total number of walks is 6*5-6 = 24.
a(26) = 0 as it is not possible to visit all 26 available lattice points when the walk starts from the middle of the box.

Crossrefs

Cf. A337023 (other box sizes), A337033 (start at center of face), A335806 (start at middle of edge), A337034 (start at corner of box), A001412, A039648.

Sequence in context: A338512 A006528 A052749 * A262445 A090574 A294842

Adjacent sequences: A337018 A337019 A337020 * A337022 A337023 A337024

Keyword

nonn,walk

Author

Scott R. Shannon, Aug 11 2020

Status

approved