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!)
A339200 Number of (undirected) Hamiltonian cycles on the n X 3 king graph. 4
4, 16, 120, 744, 4922, 31904, 208118, 1354872, 8826022, 57483536, 374412158, 2438639080, 15883563110, 103454037120, 673825180718, 4388811619032, 28585557862518, 186185731404016, 1212679737590398, 7898522254036168, 51445284278407878, 335077523213321312, 2182453613487235150, 14214930709900240312 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Seiichi Manyama, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, King Graph

Index entries for sequences related to graphs, Hamiltonian

FORMULA

Empirical g.f.: 2*x^2 * (3*x^4 + 4*x^3 + 2*x^2 - 2) / (6*x^4 + 8*x^3 + 15*x^2 + 4*x - 1). - Vaclav Kotesovec, Dec 09 2020

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 A339190(n, k):

    universe = make_nXk_king_graph(n, k)

    GraphSet.set_universe(universe)

    cycles = GraphSet.cycles(is_hamilton=True)

    return cycles.len()

def A339200(n):

    return A339190(n, 3)

print([A339200(n) for n in range(2, 20)])

CROSSREFS

Column 3 of A339190.

Cf. A339197.

Sequence in context: A332752 A210573 A337040 * A087335 A204573 A306561

Adjacent sequences:  A339197 A339198 A339199 * A339201 A339202 A339203

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 27 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 June 24 01:07 EDT 2021. Contains 345404 sequences. (Running on oeis4.)