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)])
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
Showing 1-4 of 4 results.