A339622 Number of Hamiltonian circuits within parallelograms of size 7 X n on the triangular lattice.

1, 498, 26499, 1475286, 100766213, 6523266332, 418172485806, 26971800950170, 1738936046774850, 112060168171247368, 7222422644817870197, 465494892350086836970, 30001329862709920944426, 1933604967243463575726934, 124622105764386987040047037, 8031972575008760516889720476

Offset: 2

Author

Seiichi Manyama, Dec 25 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..150
• 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)
• M. Peto, Studies of protein designability using reduced models, Thesis, 2007.

Crossrefs

Row 7 of A339849.

Cf. A145416.

Programs

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)])