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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
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
Sequence in context: A353337 A351907 A357374 * A101257 A321892 A225542
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Nov 02 2015
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)