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)])
A358869
Number of (undirected) paths in the graph C_5 X C_n.
Original entry on oeis.org
6690, 324570, 10489660, 276182500, 6486444750, 141606011050, 2938679135800, 58759814756160, 1142125726154350, 21713533582158110, 405578743418707380, 7468021173224848600, 135906384557097211050, 2449354951706961634050, 43785800216111451354800, 777390470051273329332440, 13722022446524862502553730
Offset: 2
a(2) prepended by
Ed Wynn, Jul 07 2023
A358872
Number of (undirected) paths in the graph C_6 X C_n.
Original entry on oeis.org
2298906, 136547568, 6486444750, 272445788808, 10588228608678, 390094527889632, 13820471174703870, 475213692224985720, 15959826206607422634, 525938391754196467536, 17064848263643902844850, 546612855015952410743736, 17320886593911945339408810, 543869852159220927372363456
Offset: 3
Showing 1-4 of 4 results.