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)])
A339136
Number of (undirected) cycles in the graph C_3 X P_n.
Original entry on oeis.org
1, 14, 63, 220, 701, 2154, 6523, 19640, 59001, 177094, 531383, 1594260, 4782901, 14348834, 43046643, 129140080, 387420401, 1162261374, 3486784303, 10460353100, 31381059501, 94143178714, 282429536363, 847288609320, 2541865828201, 7625597484854, 22876792454823, 68630377364740
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 A339136(n):
universe = make_CnXPk(3, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A339136(n) for n in range(1, 20)])
A339795
Number of (undirected) paths in the graph C_3 X C_n.
Original entry on oeis.org
4536, 41676, 324570, 2298906, 15340836, 98401032, 614180286, 3759485910, 22684148388, 135385868268, 801141412422, 4708188092034, 27512477620020, 160001531341584, 926684449543278, 5347897587948078, 30765345147232932, 176489253686952180, 1009897820473377654
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 A339795(n):
return B(n, 3)
print([A339795(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.