A101857 Number of possibly-self-intersecting walks that it is possible for an accelerating ant to produce with n steps (rotations & reflections not included). On step 1 the ant moves forward 1 unit, then turns left or right and proceeds 2 units, then turns left or right until at the end of its n-th step it arrives back at its starting place.

0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 16, 28, 0, 0, 0, 0, 0, 0, 1190, 2108, 0, 0, 0, 0, 0, 0

Offset

1,15

Comments

Accelerating ant walks can only arrive back at the starting place if the number of moves is -1 or 0 mod(8).

Links

Table of n, a(n) for n=1..30.

Example

a(7) = 1 because of the following solution:
655555XXX
6XXXX4XXX
6XXXX4XXX
6XXXX4XXX
6XXXX4333
6XXXXXXX2
777777712
where the ant starts at the "1" and moves right 1 space, up 2 spaces and so on...

Crossrefs

Cf. A101856.

Sequence in context: A338093 A302553 A300132 * A350302 A184039 A212051

Adjacent sequences: A101854 A101855 A101856 * A101858 A101859 A101860

Keyword

nice,nonn

Author

Gordon Hamilton, Jan 27 2005

Status

approved