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%I #22 Dec 19 2020 14:27:57
%S 12,444,7584,103184,1246892,14010212,150042016,1554630384,15735477148,
%T 156604841764,1539509238384,14997746124304,145132198165132,
%U 1397493793301476,13407313676392384,128278229316758192,1224872135665718780,11678406201771406628,111224649402691424912,1058446545979095492816
%N Number of (undirected) paths in C_4 X P_n.
%H <a href="/A338960/b338960.txt">Table of n, a(n) for n = 1..20</a>
%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 B(n, k):
%o m = k * 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, k)
%o return s
%o def A338960(n):
%o return B(4, n)
%o print([A338960(n) for n in range(1, 11)])
%Y Cf. A003752, A338709, A338961, A338962, A338963.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Dec 18 2020
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