A338962
Number of (undirected) paths in C_6 X P_n.
Original entry on oeis.org
30, 3366, 183684, 8092632, 316544562, 11481159930, 395458712832, 13123275738432, 423525613823934, 13378503050329794, 415551681048983880, 12735329289585862200, 386086186106267296494, 11601553028839397641626, 346091203382132944992240, 10262539815169483791720708
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 A(start, goal, n, k):
universe = make_CnXPk(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 A338962(n):
return B(6, n)
print([A338962(n) for n in range(1, 6)])
A338960
Number of (undirected) paths in C_4 X P_n.
Original entry on oeis.org
12, 444, 7584, 103184, 1246892, 14010212, 150042016, 1554630384, 15735477148, 156604841764, 1539509238384, 14997746124304, 145132198165132, 1397493793301476, 13407313676392384, 128278229316758192, 1224872135665718780, 11678406201771406628, 111224649402691424912, 1058446545979095492816
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 A(start, goal, n, k):
universe = make_CnXPk(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 A338960(n):
return B(4, n)
print([A338960(n) for n in range(1, 11)])
A338961
Number of (undirected) paths in C_5 X P_n.
Original entry on oeis.org
20, 1285, 39425, 971610, 21272810, 432363395, 8355404595
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 A(start, goal, n, k):
universe = make_CnXPk(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 A338961(n):
return B(5, n)
print([A338961(n) for n in range(1, 6)])
A338963
Number of (undirected) paths in C_n X P_n.
Original entry on oeis.org
1209, 103184, 21272810, 11481159930
Offset: 3
-
# 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 A(start, goal, n, k):
universe = make_CnXPk(n, k)
GraphSet.set_universe(universe)
paths = GraphSet.paths(start, goal)
return paths.len()
def A338963(n):
m = n * n
s = 0
for i in range(1, m):
for j in range(i + 1, m + 1):
s += A(i, j, n, n)
return s
print([A338963(n) for n in range(3, 7)])
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