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A339960 Number of Hamiltonian circuits within parallelograms of size 8 X n on the triangular lattice. 2
1, 1676, 183521, 20842802, 3061629439, 418172485806, 56203566442908, 7621726574570613, 1033232532941136255, 139934009951521872490, 18955155770535463735959, 2567688102114635009977537, 347811042296785583958285788, 47113523803568895604053871759, 6381875340326645360658645942215 (list; graph; refs; listen; history; text; internal format)
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 h7(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 A339960(n):
return A339849(8, n)
print([A339960(n) for n in range(2, 8)])
CROSSREFS
Row 8 of A339849.
Cf. A145418.
Sequence in context: A188008 A145755 A252300 * A252442 A159625 A156425
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 25 2020
STATUS
approved

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Last modified July 21 18:17 EDT 2024. Contains 374475 sequences. (Running on oeis4.)