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A339142
Number of (undirected) cycles in the graph C_5 X P_n.
5
1, 52, 733, 9394, 119235, 1512196, 19177677, 243212478, 3084441599, 39117172360, 496087629441, 6291429718962, 79788500460003, 1011885230273244, 12832823194696645, 162747064808635206, 2063973507784856167, 26175505197898511728, 331960206747350288969, 4209950410912939269210
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_CnXPk(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))
return grids
def A339142(n):
universe = make_CnXPk(5, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339142(n) for n in range(1, 9)])
CROSSREFS
Cf. A003731 (Hamiltonian cycles), A339117, A339136, A339137, A339140, A339143.
Sequence in context: A249712 A255945 A215365 * A264309 A160344 A163691
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 25 2020
EXTENSIONS
More terms from Ed Wynn, Jun 28 2023
STATUS
approved