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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181519 Number of torsion pairs in the cluster category of type A_n up to Auslander-Reiten translation. 1
1, 3, 5, 19, 62, 301, 1413, 7304, 38294, 208052, 1149018, 6466761, 36899604, 213245389, 1245624985, 7345962126, 43688266206, 261791220038, 1579363550250, 9586582997562, 58513327318992, 358957495385684, 2212294939905234 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

a(n) is also the number of Ptolemy diagrams on n vertices up to rotation.

a(n) is the sum over all polygon dissections up to rotation, where each region of size at least four has weight two.

LINKS

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

Thorsten Holm, Peter Jorgensen, Martin Rubey, Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A_n, arXiv:1010.1184v1 [math.RT], 2010

FORMULA

G.f.: 2 sum(phi(d)/d*log(1/(1-P(y^d))),d=1..infinity) -2/3*(P(y)^3+2*P(y^3))-1/2*(3*P(y)^2+P(y^2))-2*P(y)+y where P(y) is the G.f. for the number of torsion pairs in the cluster category of type A_n, A181517.

EXAMPLE

For n=5 there are 5 Ptolemy diagrams up to rotation: the pentagon with no diagonal, the pentagon with one diagonal, the pentagon with two noncrossing diagonals, the pentagon with three diagonals and the pentagon with all five diagonals.

CROSSREFS

Cf. A181517

Sequence in context: A174132 A106918 A182357 * A265778 A257866 A251617

Adjacent sequences:  A181516 A181517 A181518 * A181520 A181521 A181522

KEYWORD

nonn

AUTHOR

Martin Rubey (martin.rubey(AT)math.uni-hannover.de), Oct 26 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 November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)