A339960 Number of Hamiltonian circuits within parallelograms of size 8 X n on the triangular lattice.

1, 1676, 183521, 20842802, 3061629439, 418172485806, 56203566442908, 7621726574570613, 1033232532941136255, 139934009951521872490, 18955155770535463735959, 2567688102114635009977537, 347811042296785583958285788, 47113523803568895604053871759, 6381875340326645360658645942215

Offset: 2

Author

Seiichi Manyama, Dec 25 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..100
• 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)
• M. Peto, Studies of protein designability using reduced models, Thesis, 2007.

Crossrefs

Row 8 of A339849.

Cf. A145418.

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 A339960(n):
    return A339849(8, n)
print([A339960(n) for n in range(2, 8)])