A339074
Number of (undirected) cycles in the graph C_3 X C_n.
Original entry on oeis.org
312, 1531, 7298, 35205, 174268, 885719, 4601982, 24306577, 129851384, 698930787, 3780126106, 20505863069, 111441343860, 606312668335, 3300926292470, 17978225967081, 97939845566896, 533619551723963, 2907629293865874, 15844069824657013, 86338863686763692, 470492593924667271
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 A339074(n):
universe = make_CnXCk(n, 3)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339074(n) for n in range(3, 30)])
A339075
Number of (undirected) cycles in the graph C_4 X C_n.
Original entry on oeis.org
1531, 14704, 132089, 1165194, 10254423, 90693764, 808627861, 7276584222, 66085185907, 605303076120, 5585690299505, 51868931553714, 484136128508431, 4537416076416428, 42662439747995981, 402124615161547590, 3797500862839734443, 35913373920441057600, 340000796575687888937
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 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)])
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
A358855
Number of (undirected) cycles in the graph C_5 X C_n.
Original entry on oeis.org
7298, 132089, 2183490, 34846271, 548520502, 8593998133, 134605124804, 2112734282875, 33277625395316, 526401223244097, 8365394600819118, 133560895142858179, 2142023381577621160, 34497747586243864061, 557716750350292506722, 9047143455744392381123
Offset: 3
A358856
Number of (undirected) cycles in the graph C_6 X C_n.
Original entry on oeis.org
35205, 1165194, 34846271, 995818716, 27888940001, 773821636750, 21378607696815, 589724385779004, 16270311004670729, 449476421435825046, 12442365158796491483, 345293706994488530008, 9609116953522118190009, 268189777386676703675238, 7507073356371047897526119, 210735605847160867677182616
Offset: 3
A297669
Number of chordless cycles in the n X n torus grid graph.
Original entry on oeis.org
15, 224, 1815, 28716, 886837, 46775584, 4207536351
Offset: 3
Showing 1-6 of 6 results.