A264035 Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of integer partitions lambda of n such that there are k partitions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral.

1, 1, 2, 3, 5, 5, 2, 6, 4, 1, 7, 2, 3, 2, 1, 8, 2, 3, 2, 3, 3, 0, 1

Offset

0,3

Comments

Row sums give A000041.

Links

Table of n, a(n) for n=0..22.

FindStat - Combinatorial Statistic Finder, Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight.

J. De Loera and T. B. McAllister, Vertices of Gelfand-Tsetlin polytopes, arXiv:math/0309329 [math.CO], 2003, MathSciNet:2096742.

Example

Triangle begins:
1,
1,
2,
3,
5,
5,2,
6,4,1,
7,2,3,2,1,
8,2,3,2,3,3,0,1,
...

Crossrefs

Cf. A000041, A264047, A264048, A264049.

Sequence in context: A343767 A175210 A264047 * A082876 A096099 A019780

Adjacent sequences: A264032 A264033 A264034 * A264036 A264037 A264038

Keyword

nonn,tabf,more

Author

Christian Stump, Nov 01 2015

Status

approved