A227338 Number of n-step self-avoiding walks on cubic lattice ending at point with x = k.

1, 4, 1, 12, 8, 1, 44, 40, 12, 1, 172, 176, 84, 16, 1, 772, 748, 468, 144, 20, 1, 3308, 3248, 2332, 984, 220, 24, 1, 14924, 14280, 11068, 5756, 1788, 312, 28, 1, 64956, 63768, 51472, 30760, 12108, 2944, 420, 32, 1, 294252, 285296, 237832, 155912, 72948, 22732, 4516

Offset: 0

Author

Joseph Myers, Jul 07 2013

Keywords

• nonn
• walk
• tabl

Comments

The number of walks ending with x = -k is the same as the number ending with x = k.

Examples

			Initial rows (paths of length 0, 1, 2, ...):
1;
4, 1;
12, 8, 1;
44, 40, 12, 1;
...
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 0..275 (terms 0..152 from Joseph Myers)
• J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Crossrefs

Cf. A000759, A000760, A000761, A000762, A001412.

Formula

For n > 0, A001412(n) = T(n,0) + 2 * Sum_{k=1..n} T(n,k). - Bert Dobbelaere, Jan 06 2019