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A101856
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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.
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2
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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
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OFFSET
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1,16
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..30.
Eric Weisstein's World of Mathematics, Golygon .
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EXAMPLE
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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...
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CROSSREFS
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Cf. A101857, A006718.
Sequence in context: A151755 A181004 A051344 * A059484 A035678 A094518
Adjacent sequences: A101853 A101854 A101855 * A101857 A101858 A101859
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KEYWORD
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nice,nonn
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AUTHOR
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Gordon Robert Hamilton (hamiltonian(AT)shaw.ca), Jan 27 2005
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STATUS
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approved
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