cp's OEIS Frontend

A338963 Number of (undirected) paths in C_n X P_n.

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