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)])
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)])
A358869
Number of (undirected) paths in the graph C_5 X C_n.
Original entry on oeis.org
6690, 324570, 10489660, 276182500, 6486444750, 141606011050, 2938679135800, 58759814756160, 1142125726154350, 21713533582158110, 405578743418707380, 7468021173224848600, 135906384557097211050, 2449354951706961634050, 43785800216111451354800, 777390470051273329332440, 13722022446524862502553730
Offset: 2
a(2) prepended by
Ed Wynn, Jul 07 2023
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