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A338962 Number of (undirected) paths in C_6 X P_n.

%I A338962 #15 Dec 19 2020 08:05:27
%S A338962 30,3366,183684,8092632,316544562,11481159930,395458712832,
%T A338962 13123275738432,423525613823934,13378503050329794,415551681048983880,
%U A338962 12735329289585862200,386086186106267296494,11601553028839397641626,346091203382132944992240,10262539815169483791720708
%N A338962 Number of (undirected) paths in C_6 X P_n.
%o A338962 (Python)
%o A338962 # Using graphillion
%o A338962 from graphillion import GraphSet
%o A338962 def make_CnXPk(n, k):
%o A338962     grids = []
%o A338962     for i in range(1, k + 1):
%o A338962         for j in range(1, n):
%o A338962             grids.append((i + (j - 1) * k, i + j * k))
%o A338962         grids.append((i + (n - 1) * k, i))
%o A338962     for i in range(1, k * n, k):
%o A338962         for j in range(1, k):
%o A338962             grids.append((i + j - 1, i + j))
%o A338962     return grids
%o A338962 def A(start, goal, n, k):
%o A338962     universe = make_CnXPk(n, k)
%o A338962     GraphSet.set_universe(universe)
%o A338962     paths = GraphSet.paths(start, goal)
%o A338962     return paths.len()
%o A338962 def B(n, k):
%o A338962     m = k * n
%o A338962     s = 0
%o A338962     for i in range(1, m):
%o A338962         for j in range(i + 1, m + 1):
%o A338962             s += A(i, j, n, k)
%o A338962     return s
%o A338962 def A338962(n):
%o A338962     return B(6, n)
%o A338962 print([A338962(n) for n in range(1, 6)])
%Y A338962 Cf. A338709, A338960, A338961, A338963.
%K A338962 nonn
%O A338962 1,1
%A A338962 _Seiichi Manyama_, Dec 18 2020