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A264048 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 compositions mu such that the Gelfand-Tsetlin polytope for lambda and mu is integral. 3
1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,57

COMMENTS

Row sums give A000041, n >= 1.

LINKS

Table of n, a(n) for n=1..101.

FindStat - Combinatorial Statistic Finder, Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition 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,

1,0,1,1,

1,0,0,1,1,0,1,1,

1,0,0,0,1,0,1,0,0,0,1,1,0,0,1,1,

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

...

CROSSREFS

Cf. A000041, A264035, A264047, A264049.

Sequence in context: A266344 A174875 A193510 * A101257 A321892 A225542

Adjacent sequences:  A264045 A264046 A264047 * A264049 A264050 A264051

KEYWORD

nonn,tabf

AUTHOR

Christian Stump, Nov 02 2015

STATUS

approved

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Last modified July 20 11:28 EDT 2019. Contains 325180 sequences. (Running on oeis4.)