A335806 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 middle of the box's edge.

1, 4, 12, 40, 118, 358, 936, 2600, 6212, 16068, 34936, 83708, 163452, 357056, 613592, 1205716, 1770616, 3073480, 3715920, 5573480, 5255048, 6591160, 4353912, 4330096, 1513712, 1061392, 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) = 4 as the walk is free to move one step in four directions.
a(2) = 12. A first step along either edge leading to the corner leaves two possible second steps. A first step to the centre of either face can be followed by a second step to three edges or to the center of the cube, four steps in all. Thus the total number of 2-step walks is 2*2+2*4 = 12.
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's edge.

Crossrefs

Cf. A336862 (other box sizes), A337021 (start at center of box), A337033 (start at center of face), A337034 (start at corner of box), A001412, A259808, A039648.

Sequence in context: A328533 A265127 A056274 * A058353 A104525 A126986

Adjacent sequences: A335803 A335804 A335805 * A335807 A335808 A335809

Keyword

nonn,walk,fini,full

Author

Scott R. Shannon, Aug 14 2020

Status

approved