A293709 Number of Hamiltonian walks on a Sierpinski fractal.

1, 2, 10, 92, 1852, 78032, 6846876, 1255156712, 482338029046, 387869817764474, 652822489612455344, 2300645402905295350788, 16976857303773016457918252

Offset: 2

Author

Michel Marcus, Oct 25 2017

Keywords

• nonn
• walk
• more

Links

• András Kaszanyitzky, The generalized Sierpinski Arrowhead Curve, arXiv:1710.08480 [math.CO], 2017.
• András Kaszanyitzky, Triangular fractal approximating graphs and their covering paths and cycles, arXiv:1710.09475 [math.CO], 2017.
• Jelena Stajic, Suncica Elezovic-Hadzic, Hamiltonian walks on Sierpinski and n-simplex fractals, arXiv:cond-mat/0310777 [cond-mat.stat-mech], 2003-2005.

Crossrefs

Cf. A112676.

Programs

Python

# Using graphillion
from graphillion import GraphSet
def make_n_triangular_grid_graph(n):
    s = 1
    grids = []
    for i in range(n + 1, 1, -1):
        for j in range(i - 1):
            a, b, c = s + j, s + j + 1, s + i + j
            grids.extend([(a, b), (a, c), (b, c)])
        s += i
    return grids
def A293709(n):
    universe = make_n_triangular_grid_graph(n - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, n * (n + 1) // 2
    paths = GraphSet.paths(start, goal, is_hamilton=True)
    return paths.len()
print([A293709(n) for n in range(2, 10)])  # Seiichi Manyama, Dec 05 2020

Extensions

a(10)-a(14) from Seiichi Manyama, Dec 05 2020