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A272763 Number of n-step self-avoiding walks on the square lattice with diagonals allowed (Moore neighborhood). 1
1, 8, 56, 368, 2336, 14576, 89928, 550504, 3349864, 20290360, 122445504, 736685008, 4421048016, 26475370088, 158257613848, 944493430152, 5628996811904 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Moore neighborhood :

o o o

o x o

o o o

Von Neumann neighborhood (A001411):

  o

o x o

  o

Note that the path avoids already visited lattice points, but can intersect itself (two diagonal steps). A nonintersecting version is A272773.

LINKS

Table of n, a(n) for n=0..16.

MATHEMATICA

mo=Most@Tuples[{-1, 1, 0}, 2]; a[0]=1; a[tg_, p_: {{0, 0}}] := Block[{e, mv = Complement[Last[p] + # & /@ mo, p]}, If[tg == 1, Length@mv, Sum[a[tg - 1, Append[p, e]], {e, mv}]]]; a /@ Range[0, 7] (* Giovanni Resta, May 06 2016 *)

CROSSREFS

Cf. A001411, A272773.

Sequence in context: A272773 A162754 A081626 * A199939 A003494 A057084

Adjacent sequences:  A272760 A272761 A272762 * A272764 A272765 A272766

KEYWORD

nonn,walk,more

AUTHOR

Francois Alcover, May 05 2016

EXTENSIONS

a(13)-a(16) from Giovanni Resta, May 06 2016

STATUS

approved

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Last modified November 18 16:23 EST 2018. Contains 317323 sequences. (Running on oeis4.)