login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339797 Number of (undirected) Hamiltonian paths in the graph C_3 X C_n. 3
756, 4128, 18240, 73368, 277536, 1001760, 3512160, 12009480, 40390944, 133893936, 439304736, 1428450072, 4613176800, 14809528896, 47315578848, 150534443304, 477237381024, 1508232832080, 4753573999776, 14945425070136, 46886868887136, 146802927436128, 458818252975200 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..25.

Eric Weisstein's World of Mathematics, Hamiltonian Path

Eric Weisstein's World of Mathematics, Torus Grid Graph

PROG

(Python)

# 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)])

CROSSREFS

Cf. A003685, A268838, A339795, A339798.

Sequence in context: A158657 A004010 A320686 * A288779 A018898 A004048

Adjacent sequences:  A339794 A339795 A339796 * A339798 A339799 A339800

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 17 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)