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A272265 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice.

%I A272265 #40 Feb 03 2025 18:57:27
%S A272265 1,3,9,21,51,123,285,669,1569,3603,8343,19335,44193,101577,233697,
%T A272265 532569,1218345,2789475,6343161,14464101,33004269,74923059,170440203,
%U A272265 387945747,879473277,1997066751,4536975315,10273846185
%N A272265 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice.
%C A272265 Only 3 directions are allowed, separated by 120 degrees.
%C A272265   o
%C A272265   x
%C A272265 o   o
%t A272265 mo={{2, 0},{-1, 1}, {-1, -1}}; a[0]=1;
%t A272265 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}]]];
%t A272265 a /@ Range[0, 10]
%t A272265 (* _Robert FERREOL_, Nov 28 2018; after the program of Giovanni Resta in A001411 *)
%o A272265 (Python)
%o A272265 def add(L, x):
%o A272265     M=[y for y in L]; M.append(x)
%o A272265     return(M)
%o A272265 plus=lambda L, M : [x+y for x, y in zip(L, M)]
%o A272265 mo=[[2, 0], [-1, 1], [-1, -1]]
%o A272265 def a(n, P=[[0, 0]]):
%o A272265     if n==0: return(1)
%o A272265     mv1 = [plus(P[-1], x) for x in mo]
%o A272265     mv2=[x for x in mv1 if x not in P]
%o A272265     if n==1: return(len(mv2))
%o A272265     else: return(sum(a(n-1, add(P, x)) for x in mv2))
%o A272265 print([a(n) for n in range(11)])
%o A272265 # _Robert FERREOL_, Nov 30 2018
%Y A272265 Cf. A001334.
%K A272265 nonn,walk,more
%O A272265 0,2
%A A272265 _Francois Alcover_, May 05 2016