%I #19 Feb 16 2025 08:34:01
%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="https://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,changed
%O 3,1
%A _Seiichi Manyama_, Dec 17 2020