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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

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.

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

Adjacent sequences:  A339957 A339958 A339959 * A339961 A339962 A339963

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 25 2020

STATUS

approved

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Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)