A034165 Number of 'zig-zag' self-avoiding walks on an n X n lattice from a corner to opposite one.

1, 2, 2, 4, 10, 36, 188, 1582, 20576, 388592, 10461898, 408377408, 23652253982, 2052824036762, 265634749049320, 50828371798067240, 14332652975511249270, 5965063285700860583374, 3673747085941764271303790, 3352654279654465148964378096

Offset

1,2

Comments

A 'zig-zag' walk does not contain 2 consecutive steps in the same direction.

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Self-avoiding walk.

Example

a(4)=4 because of the following paths:
A._......A......A.._.......A_
...|_....|_.....|_|.|_......_|
.....|_....|_........_|....|_..._
.......|.....|_.....|_.......|_|.|
.......B.......B......B..........B

Crossrefs

Cf. A034166.

Sequence in context: A112556 A254400 A054100 * A006181 A366425 A322924

Adjacent sequences: A034162 A034163 A034164 * A034166 A034167 A034168

Keyword

nonn,walk

Author

Felice Russo

Extensions

a(7)-a(11) computed by David W. Wilson

a(12)-a(13) computed by Luca Petrone, Dec 31 2015

a(14)-a(20) from Andrew Howroyd, Jan 15 2018

Status

approved