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A293709 Number of Hamiltonian walks on a Sierpinski fractal.

%I A293709 #24 Dec 05 2020 10:22:16
%S A293709 1,2,10,92,1852,78032,6846876,1255156712,482338029046,387869817764474,
%T A293709 652822489612455344,2300645402905295350788,16976857303773016457918252
%N A293709 Number of Hamiltonian walks on a Sierpinski fractal.
%H A293709 András Kaszanyitzky, <a href="https://arxiv.org/abs/1710.08480">The generalized Sierpinski Arrowhead Curve</a>, arXiv:1710.08480 [math.CO], 2017.
%H A293709 András Kaszanyitzky, <a href="https://arxiv.org/abs/1710.09475">Triangular fractal approximating graphs and their covering paths and cycles</a>, arXiv:1710.09475 [math.CO], 2017.
%H A293709 Jelena Stajic, Suncica Elezovic-Hadzic, <a href="https://arxiv.org/abs/cond-mat/0310777">Hamiltonian walks on Sierpinski and n-simplex fractals</a>, arXiv:cond-mat/0310777 [cond-mat.stat-mech], 2003-2005.
%o A293709 (Python)
%o A293709 # Using graphillion
%o A293709 from graphillion import GraphSet
%o A293709 def make_n_triangular_grid_graph(n):
%o A293709     s = 1
%o A293709     grids = []
%o A293709     for i in range(n + 1, 1, -1):
%o A293709         for j in range(i - 1):
%o A293709             a, b, c = s + j, s + j + 1, s + i + j
%o A293709             grids.extend([(a, b), (a, c), (b, c)])
%o A293709         s += i
%o A293709     return grids
%o A293709 def A293709(n):
%o A293709     universe = make_n_triangular_grid_graph(n - 1)
%o A293709     GraphSet.set_universe(universe)
%o A293709     start, goal = 1, n * (n + 1) // 2
%o A293709     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A293709     return paths.len()
%o A293709 print([A293709(n) for n in range(2, 10)])  # _Seiichi Manyama_, Dec 05 2020
%Y A293709 Cf. A112676.
%K A293709 nonn,walk,more
%O A293709 2,2
%A A293709 _Michel Marcus_, Oct 25 2017
%E A293709 a(10)-a(14) from _Seiichi Manyama_, Dec 05 2020