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A339075
Number of (undirected) cycles in the graph C_4 X C_n.
6
1531, 14704, 132089, 1165194, 10254423, 90693764, 808627861, 7276584222, 66085185907, 605303076120, 5585690299505, 51868931553714, 484136128508431, 4537416076416428, 42662439747995981, 402124615161547590, 3797500862839734443, 35913373920441057600, 340000796575687888937
OFFSET
3,1
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
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 A339075(n):
universe = make_CnXCk(4, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339075(n) for n in range(3, 30)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 22 2020
STATUS
approved