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A264047 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 compositions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral. 3
1, 1, 2, 3, 5, 5, 2, 6, 3, 0, 1, 0, 0, 1, 7, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 8, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Row sums give A000041.
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,
2,
3,
5,
5,2,
6,3,0,1,0,0,1,
7,1,0,0,0,0,0,2,2,0,0,1,0,0,0,0,1,1,
8,1,0,0,0,0,0,0,2,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,2,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
...
CROSSREFS
Sequence in context: A118141 A343767 A175210 * A264035 A082876 A096099
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Nov 01 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)