login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339762 Number of (undirected) Hamiltonian paths in the 4 X n king graph. 4
1, 208, 4678, 171592, 4743130, 132202038, 3461461060, 88405359072, 2197293738684, 53565801482634, 1284136961473864, 30365618160010650, 709700882866473654, 16422374051280905778, 376744989106882359402, 8578133199326578887346, 194030408441913214687458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Graph Path

Eric Weisstein's World of Mathematics, King Graph

PROG

(Python)

# Using graphillion

from graphillion import GraphSet

def make_nXk_king_graph(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))

            if i < k:

                grids.append((i + (j - 1) * k, i + j * k + 1))

            if i > 1:

                grids.append((i + (j - 1) * k, i + j * k - 1))

    for i in range(1, k * n, k):

        for j in range(1, k):

            grids.append((i + j - 1, i + j))

    return grids

def A(start, goal, n, k):

    universe = make_nXk_king_graph(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 A339762(n):

    return B(n, 4)

print([A339762(n) for n in range(1, 11)])

CROSSREFS

Cf. A003695, A308129, A339760, A339761, A339763.

Sequence in context: A172967 A343507 A231111 * A223252 A223610 A184276

Adjacent sequences:  A339759 A339760 A339761 * A339763 A339764 A339765

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 16 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 July 25 09:05 EDT 2021. Contains 346286 sequences. (Running on oeis4.)