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A333863
Number of Hamiltonian paths in a 2*(2*n+1) X (2*n+1) grid starting at the upper left corner and finishing in the lower right corner.
3
1, 16, 117204, 440051896440, 825830699757513748579, 769203260676279544212492116449800, 354179806054404909542325896762875458037457353029, 80433401895946253522491939742836167238530417144721958187080077425
OFFSET
0,2
FORMULA
a(n) = A333580(2*(2*n+1), 2*n+1).
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333863(n):
universe = tl.grid(4 * n + 1, 2 * n)
GraphSet.set_universe(universe)
start, goal = 1, 2 * (2 * n + 1) ** 2
paths = GraphSet.paths(start, goal, is_hamilton=True)
return paths.len()
print([A333863(n) for n in range(7)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 08 2020
EXTENSIONS
More terms from Ed Wynn, Jun 28 2023
STATUS
approved