A306178 Number of unrooted self-avoiding walks with n steps that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4.

1, 4, 15, 86, 492, 2992, 18172, 110643, 672267, 4069122, 24578785, 147972210, 889332713, 5331980703, 31924424199

Offset: 1

Author

Hugo Pfoertner, Jun 23 2018

Keywords

• nonn
• walk
• more

Comments

The turning angles are those of the regular octagon, with one vertex corresponding to the forbidden U-turn. The path may neither intersect nor touch itself anywhere.

Links

• Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
• Hugo Pfoertner, Illustration of walks of lengths <= 3.

Crossrefs

Cf. A266925, A037245, A306175, A151541, A306177, A306179, A306180, A306181, A306182.

Extensions

a(7)-a(15) from Bert Dobbelaere, May 15 2025