A339960 - OEIS

%I #17 Dec 26 2020 02:42:07

%S 1,1676,183521,20842802,3061629439,418172485806,56203566442908,

%T 7621726574570613,1033232532941136255,139934009951521872490,

%U 18955155770535463735959,2567688102114635009977537,347811042296785583958285788,47113523803568895604053871759,6381875340326645360658645942215

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

%H Seiichi Manyama, <a href="/A339960/b339960.txt">Table of n, a(n) for n = 2..100</a>

%H Olga Bodroža-Pantić, Harris Kwong and Milan Pantić, <a href="https://doi.org/10.1016/j.dam.2015.07.028">Some new characterizations of Hamiltonian cycles in triangular grid graphs</a>, Discrete Appl. Math. 201 (2016) 1-13. (a(n) is equal to h7(n-1) defined by this paper)

%H M. Peto, <a href="https://doi.org/10.31274/rtd-180813-17105">Studies of protein designability using reduced models</a>, Thesis, 2007.

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o def make_T_nk(n, k):

%o     grids = []

%o     for i in range(1, k + 1):

%o         for j in range(1, n):

%o             grids.append((i + (j - 1) * k, i + j * k))

%o             if i < k:

%o                 grids.append((i + (j - 1) * k, i + j * k + 1))

%o     for i in range(1, k * n, k):

%o         for j in range(1, k):

%o             grids.append((i + j - 1, i + j))

%o     return grids

%o def A339849(n, k):

%o     universe = make_T_nk(n, k)

%o     GraphSet.set_universe(universe)

%o     cycles = GraphSet.cycles(is_hamilton=True)

%o     return cycles.len()

%o def A339960(n):

%o     return A339849(8, n)

%o print([A339960(n) for n in range(2, 8)])

%Y Row 8 of A339849.

%Y Cf. A145418.

%K nonn

%O 2,2

%A _Seiichi Manyama_, Dec 25 2020