The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A272265 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Only 3 directions are allowed, separated by 120 degrees.   o   x o   o LINKS 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: A262444 A109755 A005254 * A191796 A007056 A026551 Adjacent sequences:  A272262 A272263 A272264 * A272266 A272267 A272268 KEYWORD nonn,walk AUTHOR Francois Alcover, May 05 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)