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

1, 3, 9, 21, 51, 123, 285, 669, 1569, 3603, 8343, 19335, 44193, 101577, 233697, 532569, 1218345, 2789475, 6343161, 14464101, 33004269, 74923059, 170440203, 387945747, 879473277, 1997066751, 4536975315, 10273846185

Offset

0,2

Comments

Only 3 directions are allowed, separated by 120 degrees.

o

x

o o

Links

Table of n, a(n) for n=0..27.

Mathematica

mo={{2, 0}, {-1, 1}, {-1, -1}}; 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, 10]
(* Robert FERREOL, Nov 28 2018; after the program of Giovanni Resta in A001411 *)

Prog

(Python)
def add(L, x):
... M=[y for y in L]; M.append(x)
... return(M)
plus=lambda L, M : [x+y for x, y in zip(L, M)]
mo=[[2, 0], [-1, 1], [-1, -1]]
def a(n, P=[[0, 0]]):
... if n==0: return(1)
... mv1 = [plus(P[-1], x) for x in mo]
... mv2=[x for x in mv1 if x not in P]
... if n==1: return(len(mv2))
... else: return(sum(a(n-1, add(P, x)) for x in mv2))
[a(n) for n in range(11)]
# Robert FERREOL, Nov 30 2018

Crossrefs

Cf. A001334.

Sequence in context: A109755 A348403 A005254 * A191796 A367111 A372375

Adjacent sequences: A272262 A272263 A272264 * A272266 A272267 A272268

Keyword

nonn,walk

Author

Francois Alcover, May 05 2016

Status

approved