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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.
1

%I #5 Jul 27 2015 19:23:03

%S 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

%N 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.

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

%e a(7) = 1 because of the following solution:

%e 655555XXX

%e 6XXXX4XXX

%e 6XXXX4XXX

%e 6XXXX4XXX

%e 6XXXX4333

%e 6XXXXXXX2

%e 777777712

%e where the ant starts at the "1" and moves right 1 space, up 2 spaces and so on...

%Y Cf. A101856.

%K nice,nonn

%O 1,15

%A _Gordon Hamilton_, Jan 27 2005