OFFSET
2,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 2..400
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 27 2020
STATUS
approved