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)])
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)])
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)])
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
Showing 1-5 of 5 results.