A339796
Number of (undirected) paths in the graph C_4 X C_n.
Original entry on oeis.org
41676, 725408, 10489660, 136547568, 1660652028, 19269238080, 216100013292, 2362533383920, 25329574375116, 267467192029728, 2790488055689724, 28832824624840880, 295579830237167580, 3010545385659678848, 30497626012737910348, 307541698683047474544
Offset: 3
-
# 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)])
A339797
Number of (undirected) Hamiltonian paths in the graph C_3 X C_n.
Original entry on oeis.org
756, 4128, 18240, 73368, 277536, 1001760, 3512160, 12009480, 40390944, 133893936, 439304736, 1428450072, 4613176800, 14809528896, 47315578848, 150534443304, 477237381024, 1508232832080, 4753573999776, 14945425070136, 46886868887136, 146802927436128, 458818252975200
Offset: 3
-
# 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, is_hamilton=True)
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 A339797(n):
return B(n, 3)
print([A339797(n) for n in range(3, 10)])
A358868
Number of (undirected) Hamiltonian paths in the graph C_5 X C_n.
Original entry on oeis.org
1160, 18240, 287160, 2955700, 29861820, 263890620, 2271291760, 18578622510, 148166461700, 1154270708140, 8816903664840, 66466271481610, 493981029964240, 3639806487902700, 26549365603051040, 192467514066590100, 1385199533746259460, 9923453811044261140, 70715845300102361800
Offset: 2
More terms from
Ed Wynn, Jul 07 2023
A358870
Number of (undirected) Hamiltonian paths in the graph C_6 X C_n.
Original entry on oeis.org
3264, 73368, 2172480, 29861820, 560028096, 6632769528, 103075391424, 1156940480232, 16166871906480, 176333810290572, 2300510733948576, 24611138715163572, 306092489935215648, 3227108582232289260, 38755349620705085952, 403867959699992233836, 4722889110592680685152, 48750193590184268147100
Offset: 2
More terms from
Ed Wynn, Jul 07 2023
Showing 1-4 of 4 results.