A264049 Triangle read by rows: T(n,k) (n>=1, k>=1) 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 integral.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 1, 1, 3, 0, 2, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 3, 2, 2, 2, 0, 2, 0, 3, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1

Offset

1,13

Comments

Row sums give A000041, n >= 1.

Links

Table of n, a(n) for n=1..66.

FindStat - Combinatorial Statistic Finder, Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer 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,
1,1,
1,1,1,
1,1,1,1,1,
1,2,0,2,0,1,1,
1,2,1,2,0,1,1,1,0,1,1,
1,3,0,2,2,1,1,1,0,0,1,1,0,1,1,
1,3,2,2,2,0,2,0,3,0,0,2,0,0,1,0,1,0,1,0,1,1,
...

Crossrefs

Cf. A000041, A264035, A264047, A264048.

Sequence in context: A339896 A112712 A026608 * A287337 A026612 A287341

Adjacent sequences: A264046 A264047 A264048 * A264050 A264051 A264052

Keyword

nonn,tabf

Author

Christian Stump, Nov 02 2015

Status

approved