A339143
Number of (undirected) cycles in the graph C_6 X P_n.
Original entry on oeis.org
1, 94, 2301, 53644, 1248517, 29059380, 676374187, 15743068612, 366430841199, 8528932801462, 198516848612143, 4620617865735414, 107548097901476485, 2503256858519071030, 58265046263626611537, 1356159518571223920304, 31565557014929042873017
Offset: 1
-
# 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 A339143(n):
universe = make_CnXPk(6, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339143(n) for n in range(1, 20)])
A339137
Number of (undirected) cycles in the graph C_4 X P_n.
Original entry on oeis.org
1, 28, 225, 1540, 10217, 67388, 444017, 2925140, 19270105, 126946444, 836290209, 5509263332, 36293601737, 239092863324, 1575081964113, 10376232739316, 68355938510649, 450311249502892, 2966534083948417, 19542759549039748, 128742647137776169, 848123272992954492
Offset: 1
-
# 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 A339137(n):
universe = make_CnXPk(4, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339137(n) for n in range(1, 20)])
A339140
Number of (undirected) cycles in the graph C_n X P_n.
Original entry on oeis.org
6, 63, 1540, 119235, 29059380, 21898886793, 50826232189144, 361947451544923557, 7884768474166076906420, 524518303312357729182869149, 106448798893410608983300257207398, 65866487708413725073741586390176988083, 124207126413825808953168887580780401519104028
Offset: 2
If we represent each vertex with o, used edges with lines and unused edges with dots, and repeat the wraparound edges on left and right, the a(2) = 6 solutions for n = 2 are:
.o-o. -o.o- .o-o. -o.o- -o-o- .o.o.
| | | | | | | | . . . .
.o-o. .o-o. -o.o- -o.o- .o.o. -o-o-
-
# 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 A339140(n):
universe = make_CnXPk(n, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339140(n) for n in range(3, 7)])
a(2), a(9), a(11) and a(13)-a(18) from
Ed Wynn, Jun 25 2023
A339142
Number of (undirected) cycles in the graph C_5 X P_n.
Original entry on oeis.org
1, 52, 733, 9394, 119235, 1512196, 19177677, 243212478, 3084441599, 39117172360, 496087629441, 6291429718962, 79788500460003, 1011885230273244, 12832823194696645, 162747064808635206, 2063973507784856167, 26175505197898511728, 331960206747350288969, 4209950410912939269210
Offset: 1
-
# 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)])
More terms from
Ed Wynn, Jun 28 2023
Showing 1-4 of 4 results.