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%I #17 Dec 19 2020 08:05:35
%S 1209,103184,21272810,11481159930
%N Number of (undirected) paths in C_n X P_n.
%C a(8) = 70244258770074672.
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o def make_CnXPk(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 grids.append((i + (n - 1) * k, i))
%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 A(start, goal, n, k):
%o universe = make_CnXPk(n, k)
%o GraphSet.set_universe(universe)
%o paths = GraphSet.paths(start, goal)
%o return paths.len()
%o def A338963(n):
%o m = n * n
%o s = 0
%o for i in range(1, m):
%o for j in range(i + 1, m + 1):
%o s += A(i, j, n, n)
%o return s
%o print([A338963(n) for n in range(3, 7)])
%Y Cf. A268894, A338709, A338960, A338961, A338962.
%K nonn,more
%O 3,1
%A _Seiichi Manyama_, Dec 18 2020
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