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%I #29 Dec 26 2020 02:41:53
%S 1,498,26499,1475286,100766213,6523266332,418172485806,26971800950170,
%T 1738936046774850,112060168171247368,7222422644817870197,
%U 465494892350086836970,30001329862709920944426,1933604967243463575726934,124622105764386987040047037,8031972575008760516889720476
%N Number of Hamiltonian circuits within parallelograms of size 7 X n on the triangular lattice.
%H Seiichi Manyama, <a href="/A339622/b339622.txt">Table of n, a(n) for n = 2..150</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 h6(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 A339622(n):
%o return A339849(7, n)
%o print([A339622(n) for n in range(2, 8)])
%Y Row 7 of A339849.
%Y Cf. A145416.
%K nonn
%O 2,2
%A _Seiichi Manyama_, Dec 25 2020