A323857 Sum of end-to-end Manhattan distances over all self-avoiding n-step walks on 4-d cubic lattice.

1, 14, 135, 1144, 9083, 69690, 522781, 3864524, 28243251, 204687550, 1473038447, 10542725976, 75096139471, 532846305962, 3767808141891, 26566180648012, 186826646453453

Offset: 1

Author

Hugo Pfoertner, Feb 03 2019

Keywords

• nonn
• walk
• more

Comments

The first step is kept fixed, i.e., (0,0,0,0) -> (1,0,0,0).

Examples

			a(3) = 135, because there are 6 (of A010575(3)/8=49) end points with Manhattan distance 1, (0,-1,0,0), (0,1,0,0), (0,0,-1,0), (0,0,1,0), (0,0,0,-1), (0,0,0,1), and the remaining 43 end points all have Manhattan distance 3, e.g., (3,0,0,0), (2,-1,0,0), ..., (1,-1,-1,0), ... 135 = 6*1 + 43*3.
		

Crossrefs

Cf. A010575, A079156, A242355, A323856.