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A339796 Number of (undirected) paths in the graph C_4 X C_n. 5
41676, 725408, 10489660, 136547568, 1660652028, 19269238080, 216100013292, 2362533383920, 25329574375116, 267467192029728, 2790488055689724, 28832824624840880, 295579830237167580, 3010545385659678848, 30497626012737910348, 307541698683047474544 (list; graph; refs; listen; history; text; internal format)
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 A339796(n):
return B(n, 4)
print([A339796(n) for n in range(3, 10)])
CROSSREFS
Cf. A339075, A339798 (Hamiltonian paths).
Sequence in context: A031669 A028239 A248445 * A251978 A258689 A258685
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 17 2020
STATUS
approved

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Last modified June 19 18:42 EDT 2024. Contains 373507 sequences. (Running on oeis4.)