[seqfan] a new lattice walk
David Scambler
dscambler at bmm.com
Wed May 8 15:56:43 CEST 2013
I am surprised that superseeker does not find a formula for this deceptively simple scenario.
2-D lattice walk of length 2n beginning and ending at the origin, using steps in {NSEW} starting with East, then always moving straight ahead or turning left.
1,0,1,3,9,30,103,357,1257,4494,16246,59246,217719, ...
e.g. n=2 a(2)=1
ENWS
e.g. n=3 a(3)=3
EENWWS
ENNWSS
ENWWSE
e.g. n=4 a(4) = 9
EEENWWWS
EENNWWSS
EENWWWSE
ENNNWSSS
ENNWWSSE
ENWWWSEE
ENWWSSEN
ENWSSENW
ENWSENWS
Note: paths do not have to be self avoiding.
dave
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