A227715 Triangle read by rows: Number of 2n-step self-avoiding walks on diamond lattice ending at point with x = 2k.

1, 4, 4, 28, 24, 16, 188, 188, 128, 64, 1428, 1368, 1120, 640, 256, 10708, 10572, 8864, 6208, 3072, 1024, 82948, 81376, 71572, 53376, 32768, 14336, 4096, 644788, 637148, 570512, 453424, 304640, 166912, 65536, 16384, 5067404, 5007560, 4572076, 3762672, 2728256, 1669120

Offset

0,2

Comments

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

Links

Bert Dobbelaere, Table of n, a(n) for n = 0..135 (terms 0..77 from Joseph Myers)

J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Example

Initial rows (paths of length 0, 2, 4, ...):
{ 1 };
{ 4, 4 };
{ 28, 24, 16 };
{ 188, 188, 128, 64 }.

Crossrefs

Cf. A001394, A001395, A001396, A001397, A001398, A227716.

Sequence in context: A110139 A078146 A066836 * A173049 A272040 A338672

Adjacent sequences: A227712 A227713 A227714 * A227716 A227717 A227718

Keyword

nonn,walk,tabl

Author

Joseph Myers, Jul 21 2013

Status

approved