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A339202
Number of (undirected) Hamiltonian cycles on the n X 5 king graph.
5
16, 744, 50354, 2462064, 139472532, 7621612496, 420570135944, 23122750594160, 1272913614363472, 70046421764651488, 3855022666171830728, 212153410644220498768, 11675594777180367650512, 642548778638303396036528, 35361754611803652243506632, 1946082778374581215370587632
OFFSET
2,1
LINKS
Vaclav Kotesovec, Empirical g.f.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, King Graph
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_nXk_king_graph(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
if i < k:
grids.append((i + (j - 1) * k, i + j * k + 1))
if i > 1:
grids.append((i + (j - 1) * k, i + j * k - 1))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
def A339190(n, k):
universe = make_nXk_king_graph(n, k)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles(is_hamilton=True)
return cycles.len()
def A339202(n):
return A339190(n, 5)
print([A339202(n) for n in range(2, 20)])
CROSSREFS
Column 5 of A339190.
Cf. A339199.
Sequence in context: A209537 A086701 A218297 * A307923 A159375 A221527
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 27 2020
STATUS
approved