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%I #35 Dec 11 2018 02:05:58
%S 1,3,9,21,51,123,285,669,1569,3603,8343,19335,44193,101577,233697,
%T 532569,1218345,2789475,6343161,14464101,33004269,74923059,170440203,
%U 387945747,879473277,1997066751,4536975315,10273846185
%N Number of n-step tri-directional self-avoiding walks on the hexagonal lattice.
%C Only 3 directions are allowed, separated by 120 degrees.
%C o
%C x
%C o o
%t mo={{2, 0},{-1, 1}, {-1, -1}}; a[0]=1;
%t 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 a /@ Range[0, 10]
%t (* _Robert FERREOL_, Nov 28 2018; after the program of Giovanni Resta in A001411 *)
%o (Python)
%o def add(L,x):
%o ... M=[y for y in L];M.append(x)
%o ... return(M)
%o plus=lambda L,M : [x+y for x,y in zip(L,M)]
%o mo=[[2,0],[-1,1],[-1, -1]]
%o def a(n,P=[[0, 0]]):
%o ... if n==0: return(1)
%o ... mv1 = [plus(P[-1],x) for x in mo]
%o ... mv2=[x for x in mv1 if x not in P]
%o ... if n==1: return(len(mv2))
%o ... else: return(sum(a(n-1,add(P,x)) for x in mv2))
%o [a(n) for n in range(11)]
%o # _Robert FERREOL_, Nov 30 2018
%Y Cf. A001334.
%K nonn,walk
%O 0,2
%A _Francois Alcover_, May 05 2016
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