This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A101856 Number of non-intersecting polygons 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. 2
 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 25, 67, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS This walk by an accelerating ant can only arrive back at the starting point after n steps where n is 0 or -1 mod(8). Golygon: "A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the east or west, the third is three units to the north or south, etc. and continuing until the origin is again reached. No crossing or backtracking is allowed. The simplest golygon is (0, 0), (0, 1), (2, 1), (2, -2), (-2, -2), (-2, -7), (-8, -7), (-8, 0), (0, 0)." Weisstein. - Jonathan Vos Post, Jan 31 2005 REFERENCES Dudeney, A. K. "An Odd Journey Along Even Roads Leads to Home in Golygon City." Sci. Amer. 263, 118-121, 1990. Sallows, L. C. F. "New Pathways in Serial Isogons." Math. Intell. 14, 55-67, 1992. Sallows, L.; Gardner, M.; Guy, R. K.; and Knuth, D. "Serial Isogons of 90 Degrees." Math Mag. 64, 315-324, 1991. LINKS Eric Weisstein's World of Mathematics, Golygon . EXAMPLE For 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. A101857, A006718. Sequence in context: A151755 A181004 A051344 * A059484 A035678 A094518 Adjacent sequences:  A101853 A101854 A101855 * A101857 A101858 A101859 KEYWORD nice,nonn AUTHOR Gordon Robert Hamilton (hamiltonian(AT)shaw.ca), Jan 27 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 24 16:12 EDT 2013. Contains 225624 sequences.