A222199
Number of Hamiltonian cycles in the graph C_n X C_n.
Original entry on oeis.org
48, 1344, 23580, 3273360, 257165468, 171785923808, 61997157648756, 196554899918485160
Offset: 3
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Table[Length[FindHamiltonianCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], All]], {n, 3, 6}] (* Eric W. Weisstein, Dec 16 2023 *)
A296527
Number of (undirected) cycles in the n X n torus grid graph.
Original entry on oeis.org
312, 14704, 2183490, 995818716, 1383238940818, 5846378997135040, 75162787766308673244
Offset: 3
-
Table[Length[FindCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All]], {n, 3, 5}] (* Eric W. Weisstein, Dec 16 2023 *)
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# 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 A296527(n):
universe = make_CnXCk(n, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
print([A296527(n) for n in range(3, 7)]) # Seiichi Manyama, Nov 22 2020
a(8)-a(9) from
Ed Wynn, Jun 28 2023
A268894
Number of Hamiltonian paths in C_n X P_n.
Original entry on oeis.org
1, 4, 144, 4016, 152230, 14557092, 1966154260, 761411682704, 411068703517542, 684434716944151900, 1572754514153890134760, 11579615738168536799184984, 117186519917858266359631481672, 3877921919790491112398750141807648, 176258463464553583688099296874564393850, 26493868301658838913487471166447301509560736
Offset: 1
A339797
Number of (undirected) Hamiltonian paths in the graph C_3 X C_n.
Original entry on oeis.org
756, 4128, 18240, 73368, 277536, 1001760, 3512160, 12009480, 40390944, 133893936, 439304736, 1428450072, 4613176800, 14809528896, 47315578848, 150534443304, 477237381024, 1508232832080, 4753573999776, 14945425070136, 46886868887136, 146802927436128, 458818252975200
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, is_hamilton=True)
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 A339797(n):
return B(n, 3)
print([A339797(n) for n in range(3, 10)])
A339798
Number of (undirected) Hamiltonian paths in the graph C_4 X C_n.
Original entry on oeis.org
4128, 45696, 287160, 2172480, 11866848, 76468352, 390714840, 2301083680, 11288784144, 62812654272, 299720429528, 1604776566400, 7505573487360, 39105991164160, 180179056818584, 920223907284960, 4191443432295472, 21088555826121280, 95195388883597464, 473503955161244480
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, is_hamilton=True)
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 A339798(n):
return B(n, 4)
print([A339798(n) for n in range(3, 10)])
A358868
Number of (undirected) Hamiltonian paths in the graph C_5 X C_n.
Original entry on oeis.org
1160, 18240, 287160, 2955700, 29861820, 263890620, 2271291760, 18578622510, 148166461700, 1154270708140, 8816903664840, 66466271481610, 493981029964240, 3639806487902700, 26549365603051040, 192467514066590100, 1385199533746259460, 9923453811044261140, 70715845300102361800
Offset: 2
More terms from
Ed Wynn, Jul 07 2023
A358870
Number of (undirected) Hamiltonian paths in the graph C_6 X C_n.
Original entry on oeis.org
3264, 73368, 2172480, 29861820, 560028096, 6632769528, 103075391424, 1156940480232, 16166871906480, 176333810290572, 2300510733948576, 24611138715163572, 306092489935215648, 3227108582232289260, 38755349620705085952, 403867959699992233836, 4722889110592680685152, 48750193590184268147100
Offset: 2
More terms from
Ed Wynn, Jul 07 2023
A276291
Number of directed Hamiltonian paths on the n X n torus grid graph.
Original entry on oeis.org
1512, 91392, 5911400, 1120056192, 252824095384, 187568248374272
Offset: 3
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