A359133
Sum of square end-to-end displacements over all n-step self-avoiding walks of A359741.
Original entry on oeis.org
0, 6, 24, 78, 384, 8190, 8472, 178110, 193824, 4231662, 7072056, 102812142, 208526592, 2508914454, 5268441144, 62304671286, 124116667488, 1547651742990, 2850706506936, 38100453950670
Offset: 0
A359709
Number of n-step self-avoiding walks on a 2D square lattice whose end-to-end distance is an integer.
Original entry on oeis.org
1, 4, 4, 12, 28, 76, 164, 732, 1044, 4924, 6724, 30636, 43972, 190516, 313996, 1197908, 2284260, 7678188, 16257604, 50524252, 113052396, 341811828, 773714436, 2358452388, 5245994292, 16447462492, 35395532236, 115129727188, 238542983748, 804980005276
Offset: 0
a(3) = 12 as, in the first quadrant, there is one 3-step SAW whose end-to-end distance is an integer (1 unit):
.
X---.
|
X---.
.
This can be walked in 8 different ways on a 2D square lattice. There are also the four walks directly along the x and y axes, giving a total of 8 + 4 = 12 walks.
Showing 1-2 of 2 results.
Comments