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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. 3
1, 1, 2, 3, 5, 5, 2, 6, 4, 1, 7, 2, 3, 2, 1, 8, 2, 3, 2, 3, 3, 0, 1 (list; graph; refs; listen; history; text; internal format)
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: A118141 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

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Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)