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

%I A339622 #29 Dec 26 2020 02:41:53
%S A339622 1,498,26499,1475286,100766213,6523266332,418172485806,26971800950170,
%T A339622 1738936046774850,112060168171247368,7222422644817870197,
%U A339622 465494892350086836970,30001329862709920944426,1933604967243463575726934,124622105764386987040047037,8031972575008760516889720476
%N A339622 Number of Hamiltonian circuits within parallelograms of size 7 X n on the triangular lattice.
%H A339622 Seiichi Manyama, <a href="/A339622/b339622.txt">Table of n, a(n) for n = 2..150</a>
%H A339622 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 A339622 M. Peto, <a href="https://doi.org/10.31274/rtd-180813-17105">Studies of protein designability using reduced models</a>, Thesis, 2007.
%o A339622 (Python)
%o A339622 # Using graphillion
%o A339622 from graphillion import GraphSet
%o A339622 def make_T_nk(n, k):
%o A339622     grids = []
%o A339622     for i in range(1, k + 1):
%o A339622         for j in range(1, n):
%o A339622             grids.append((i + (j - 1) * k, i + j * k))
%o A339622             if i < k:
%o A339622                 grids.append((i + (j - 1) * k, i + j * k + 1))
%o A339622     for i in range(1, k * n, k):
%o A339622         for j in range(1, k):
%o A339622             grids.append((i + j - 1, i + j))
%o A339622     return grids
%o A339622 def A339849(n, k):
%o A339622     universe = make_T_nk(n, k)
%o A339622     GraphSet.set_universe(universe)
%o A339622     cycles = GraphSet.cycles(is_hamilton=True)
%o A339622     return cycles.len()
%o A339622 def A339622(n):
%o A339622     return A339849(7, n)
%o A339622 print([A339622(n) for n in range(2, 8)])
%Y A339622 Row 7 of A339849.
%Y A339622 Cf. A145416.
%K A339622 nonn
%O A339622 2,2
%A A339622 _Seiichi Manyama_, Dec 25 2020