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!)
A255918 Array a(n,m) read by descending antidiagonals giving the number of intervals in a generalized Tamari lattice of m-ballot paths of size n. 0
1, 1, 1, 1, 3, 1, 1, 6, 13, 1, 1, 10, 58, 68, 1, 1, 15, 170, 703, 399, 1, 1, 21, 395, 3685, 9729, 2530, 1, 1, 28, 791, 13390, 91881, 146916, 16965, 1, 1, 36, 1428, 38591, 524256, 2509584, 2359968, 118668, 1, 1, 45, 2388, 94738, 2180262, 22533126 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

This array occurs in counting the degeneracies in the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. See Cordova and Shao, 1.4. - Peter Bala, Oct 29 2017

LINKS

Table of n, a(n) for n=1..51.

Olivier Bernardi and Nicolas Bonichon, Intervals in Catalan lattices and realizers of triangulations, Journal of Combinatorial Theory, Series A 116:1 (2009), pp. 55-75.

M. Bousquet-Mélou, E. Fusy, L.-F. Préville Ratelle, The number of intervals in the m-Tamari lattices, arXiv:1106.1498 [math.CO], The Electronic Journal of Combinatorics 18, 2 (2011) P31.

Clay Cordova and Shu-Heng Shao, Counting Trees in Supersymmetric Quantum Mechanics arXiv:1502.08050v2 [hep-th], 2015.

FORMULA

a(n,m) = ((m + 1)/(n*(m*n + 1)))*binomial((m + 1)^2*n + m, n - 1).

EXAMPLE

Array begins:

1,   1,    1,     1,      1,       1,       1,        1,        1, ...

1,   3,    6,    10,     15,      21,      28,       36,       45, ...

1,  13,   58,   170,    395,     791,    1428,     2388,     3765, ...

1,  68,  703,  3685,  13390,   38591,   94738,   206718,   412095, ...

1, 399, 9729, 91881, 524256, 2180262, 7291550, 20787390, 52450587, ...

...

2nd row is A000217 (triangular numbers);

3rd row is A103220;

4th row is not in the OEIS;

2nd column is A000260 (number of intervals in the usual Tamari lattice of size n);

3rd column is not in the OEIS.

MATHEMATICA

a[n_, m_] := ((m + 1)/(n*(m*n + 1)))*Binomial[(m + 1)^2*n + m, n - 1]; Table[a[n - m, m], {n, 1, 12}, {m, n - 1, 0, -1}] // Flatten

CROSSREFS

Cf. A000217, A000260, A070914 (generalized Catalan numbers giving the number of paths), A103220.

Sequence in context: A235114 A272866 A228899 * A102479 A228902 A053193

Adjacent sequences:  A255915 A255916 A255917 * A255919 A255920 A255921

KEYWORD

nonn,tabl,easy

AUTHOR

Jean-François Alcover, Mar 11 2015

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 August 10 12:39 EDT 2020. Contains 336379 sequences. (Running on oeis4.)