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A339795
Number of (undirected) paths in the graph C_3 X C_n.
5
4536, 41676, 324570, 2298906, 15340836, 98401032, 614180286, 3759485910, 22684148388, 135385868268, 801141412422, 4708188092034, 27512477620020, 160001531341584, 926684449543278, 5347897587948078, 30765345147232932, 176489253686952180, 1009897820473377654
OFFSET
3,1
LINKS
Eric Weisstein's World of Mathematics, Torus Grid Graph
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_CnXCk(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
grids.append((i + (n - 1) * k, i))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
grids.append((i + k - 1, i))
return grids
def A(start, goal, n, k):
universe = make_CnXCk(n, k)
GraphSet.set_universe(universe)
paths = GraphSet.paths(start, goal)
return paths.len()
def B(n, k):
m = k * n
s = 0
for i in range(1, m):
for j in range(i + 1, m + 1):
s += A(i, j, n, k)
return s
def A339795(n):
return B(n, 3)
print([A339795(n) for n in range(3, 10)])
CROSSREFS
Cf. A339074, A339797 (Hamiltonian paths).
Sequence in context: A235852 A138731 A250450 * A337314 A234171 A262848
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 17 2020
STATUS
approved