A339796 - OEIS

%I #15 Dec 05 2022 06:23:26

%S 41676,725408,10489660,136547568,1660652028,19269238080,216100013292,

%T 2362533383920,25329574375116,267467192029728,2790488055689724,

%U 28832824624840880,295579830237167580,3010545385659678848,30497626012737910348,307541698683047474544

%N Number of (undirected) paths in the graph C_4 X C_n.

%H Seiichi Manyama, <a href="/A339796/b339796.txt">Table of n, a(n) for n = 3..37</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o def make_CnXCk(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         grids.append((i + k - 1, i))

%o     return grids

%o def A(start, goal, n, k):

%o     universe = make_CnXCk(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 A339796(n):

%o     return B(n, 4)

%o print([A339796(n) for n in range(3, 10)])

%Y Cf. A307919, A339795, A358869, A358872.

%Y Cf. A339075, A339798 (Hamiltonian paths).

%K nonn

%O 3,1

%A _Seiichi Manyama_, Dec 17 2020