login
A339622
Number of Hamiltonian circuits within parallelograms of size 7 X n on the triangular lattice.
2
1, 498, 26499, 1475286, 100766213, 6523266332, 418172485806, 26971800950170, 1738936046774850, 112060168171247368, 7222422644817870197, 465494892350086836970, 30001329862709920944426, 1933604967243463575726934, 124622105764386987040047037, 8031972575008760516889720476
OFFSET
2,2
LINKS
Olga Bodroža-Pantić, Harris Kwong and Milan Pantić, Some new characterizations of Hamiltonian cycles in triangular grid graphs, Discrete Appl. Math. 201 (2016) 1-13. (a(n) is equal to h6(n-1) defined by this paper)
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_T_nk(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))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
def A339849(n, k):
universe = make_T_nk(n, k)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles(is_hamilton=True)
return cycles.len()
def A339622(n):
return A339849(7, n)
print([A339622(n) for n in range(2, 8)])
CROSSREFS
Row 7 of A339849.
Cf. A145416.
Sequence in context: A235753 A235528 A277785 * A073928 A045299 A106761
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 25 2020
STATUS
approved