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 A272763 Number of n-step self-avoiding walks on the square lattice with diagonals allowed (Moore neighborhood). 2
 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. The Moore neighborhood characterizes king tours. # Rainer Rosenthal, Jan 05 2019 LINKS MAPLE # For starting point stp and list Ldir of n directions (1..8) # construct the points of the whole path and count them. # If there are n+1 then the path is self-avoiding. isSelfAvoiding := proc(Ldir) local Delta, dir, ep, path;    Delta := [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]];    ep := [0, 0]; path := {ep};    for dir in Ldir do       ep := ep + Delta[dir];       path := {op(path), ep};    od;    return evalb(nops(path)=nops(Ldir)+1); end: # Count only king tours which are self-avoiding A272763 := proc(n) local count, T, p;    count := 0:    T := combinat[cartprod]([seq([\$1..8], j=1..n)]):    while not T[finished] do       p := T[nextvalue]();       if isSelfAvoiding(p) then count := count+1; fi;    od:    return count; end: # Rainer Rosenthal, Jan 05 2019 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, A300665. 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 May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)