[seqfan] a new lattice walk

[David Scambler]

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