A323856 Sum of square displacements over all self-avoiding n-step walks on 4-d cubic lattice with first step specified, A242355(n)/8.

1, 16, 177, 1696, 14995, 126180, 1025707, 8133544, 63274143, 484966972, 3672258385, 27533213880, 204715798387, 1511417062948, 11090886972237, 80957709527896, 588206815480213, 4256231985648516, 30685328305245631, 220504966309520728, 1579874958814261407

Offset

1,2

References

For references and links see A010575 and A242355.

Links

Table of n, a(n) for n=1..21.

Example

a(1) = 1 is the square displacement of the fixed initial step.
a(2) = 16, because one of the A010575(2)/8 = 7 end points is (2,0,0,0) with square distance 4 and the other 6 end points (1,-1,0,0), (1,1,0,0), (1,0,-1,0), (1,0,1,0), (1,0,0,-1), (1,0,0,1) all have square distance 2. 16 = 1*4 + 6*2.
a(3) = 177, because there are 6 end points with square distance 1, e.g., (0,1,0,0), 24 end points with square distance 3, e.g., (1,1,1,0), 18 end points with square distance 5, e.g., (2,1,0,0), and 1 end point with square distance 9, (3,0,0,0). 177 = 6*1 + 24*3 + 18*5 + 1*9.

Crossrefs

Cf. A010575, A078605, A118313, A242355, A323857.

Sequence in context: A231127 A007144 A017521 * A226507 A264297 A002399

Adjacent sequences: A323853 A323854 A323855 * A323857 A323858 A323859

Keyword

nonn,walk

Author

Hugo Pfoertner, Feb 03 2019

Status

approved