|
|
A180582
|
|
Number of Hamiltonian cycles in C_6 X P_n.
|
|
5
|
|
|
1, 8, 86, 776, 7010, 63674, 578090, 5247824, 47640092, 432480632, 3926091512, 35641352528, 323554871864, 2937255393440, 26664624744320, 242063463190976, 2197470272854016, 19948799940346880, 181096701955896896, 1644009442040416928, 14924441010395894048, 135485194778650515104
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(1) = 1, a(2) = 8, a(3) = 86, a(4) = 776, a(5) = 7010, a(6) = 63674, a(7) = 578090, a(8) = 5247824 and a(n) = -12*a(n-7) - 32*a(n-6) - 36*a(n-5) - 28*a(n-4) + 10*a(n-3) + 9*a(n-1), n>8.
G.f.: x*(x +1)*(6*x^6 -14*x^5 -2*x^4 -24*x^3 +16*x^2 -2*x +1)/(12*x^7 +32*x^6 +36*x^5 +28*x^4 -10*x^3 -9*x +1). [Colin Barker, Sep 01 2012]
|
|
PROG
|
(PARI)
a(n) = if(n<1, 0, if(n<=8, [1, 8, 86, 776, 7010, 63674, 578090, 5247824][n], -12*a(n-7) - 32*a(n-6) - 36*a(n-5) - 28*a(n-4) + 10*a(n-3) + 9*a(n-1) ) );
(Python)
# 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
universe = make_CnXPk(6, n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles(is_hamilton=True)
return cycles.len()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|