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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178435 Number of acyclic orientations of the Triangle Graph of order n. 11
1, 6, 162, 19602, 10619910, 25753129470, 279488630719746, 13573527285845525634, 2949851294016821586137934, 2868652614504623418332698354038, 12483073717920041560887416137620435882, 243068197882943244196175524589364487906969746, 21178547618859581967063811182618272071362317831449326 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Triangle Graph of order n has n rows with i vertices in row i. 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.

An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.

LINKS

Table of n, a(n) for n=1..13.

Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8

Eric Weisstein's World of Mathematics, Triangle Graph

Wikipedia, Chromatic polynomial

CROSSREFS

Cf. A182797, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796, A182798, A000217.

Sequence in context: A280477 A078535 A177781 * A183254 A143534 A104729

Adjacent sequences:  A178432 A178433 A178434 * A178436 A178437 A178438

KEYWORD

hard,nonn

AUTHOR

Alois P. Heinz, Dec 21 2010

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 December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)