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!)
A174589 Number of directed Hamiltonian cycles in the n X n X n triangular grid. 2
1, 2, 2, 6, 52, 948, 34428, 2742908, 463849560, 164734305828, 123437602332804, 194965649426622884, 647793073112134906932, 4525859704558897642199864, 66463181964865873238784109324, 2050514181580724375252309339543868, 132859453756787302153653327942753178068 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The n X n X n triangular grid has n rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.
LINKS
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
FORMULA
For n>1, a(n) = 2*A112676(n).
EXAMPLE
For n = 4 the 4 X 4 X 4 triangular grid has 10 vertices and 18 edges. If vertices are numbered from left to right in each row and ascending with row numbers, the a(4) = 6 Hamiltonian cycles are (1,2,4,7,8,5,9,10,6,3), (1,2,4,7,8,9,10,6,5,3), (1,2,5,4,7,8,9,10,6,3), (1,3,5,6,10,9,8,7,4,2), (1,3,6,10,9,5,8,7,4,2), (1,3,6,10,9,8,7,4,5,2).
CROSSREFS
Sequence in context: A032117 A137244 A284707 * A326942 A247943 A329571
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 29 2010
EXTENSIONS
a(11)-a(16) computed from A112676 by Max Alekseyev, Jul 01 2016
a(17) via A112676 from Alois P. Heinz, Jul 31 2023
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)