A339795 - OEIS

%I #18 Dec 04 2022 13:06:43

%S 4536,41676,324570,2298906,15340836,98401032,614180286,3759485910,

%T 22684148388,135385868268,801141412422,4708188092034,27512477620020,

%U 160001531341584,926684449543278,5347897587948078,30765345147232932,176489253686952180,1009897820473377654

%N Number of (undirected) paths in the graph C_3 X C_n.

%H Seiichi Manyama, <a href="/A339795/b339795.txt">Table of n, a(n) for n = 3..50</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 A339795(n):

%o     return B(n, 3)

%o print([A339795(n) for n in range(3, 10)])

%Y Cf. A307919, A339796, A358869, A358872.

%Y Cf. A339074, A339797 (Hamiltonian paths).

%K nonn

%O 3,1

%A _Seiichi Manyama_, Dec 17 2020