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 A339849 Square array T(n,k), n >= 2, k >= 2, read by antidiagonals, where T(n,k) is the number of Hamiltonian circuits within parallelograms of size n X k on the triangular lattice. 11
 1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 44, 80, 44, 1, 1, 148, 549, 549, 148, 1, 1, 498, 3851, 7104, 3851, 498, 1, 1, 1676, 26499, 104100, 104100, 26499, 1676, 1, 1, 5640, 183521, 1475286, 3292184, 1475286, 183521, 5640, 1, 1, 18980, 1269684, 20842802, 100766213, 100766213, 20842802, 1269684, 18980, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 LINKS Seiichi Manyama, Antidiagonals n = 2..13, flattened M. Peto, Studies of protein designability using reduced models, Thesis, 2007. FORMULA T(n,k) = T(k,n). EXAMPLE Square array T(n,k) begins:   1,   1,     1,       1,         1,          1, ...   1,   4,    13,      44,       148,        498, ...   1,  13,    80,     549,      3851,      26499, ...   1,  44,   549,    7104,    104100,    1475286, ...   1, 148,  3851,  104100,   3292184,  100766213, ...   1, 498, 26499, 1475286, 100766213, 6523266332, ... 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() print([A339849(j + 2, i - j + 2) for i in range(11 - 1) for j in range(i + 1)]) CROSSREFS Rows and columns 3..10 give A339850, A339851, A339852, A338970, A339622, A339960, A339961, A339962. Main diagonal gives A339854. Cf. A339190. Sequence in context: A212801 A147565 A022167 * A064281 A267318 A050154 Adjacent sequences:  A339846 A339847 A339848 * A339850 A339851 A339852 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Dec 19 2020 STATUS approved

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Last modified June 22 19:11 EDT 2021. Contains 345388 sequences. (Running on oeis4.)