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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

Table of n, a(n) for n=0..85.

FindStat - Combinatorial Statistic Finder, Number of non-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,

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

Cf. A000041, A264035, A264048, A264049.

Sequence in context: A235610 A118141 A175210 * A264035 A082876 A096099

Adjacent sequences:  A264044 A264045 A264046 * A264048 A264049 A264050

KEYWORD

nonn,tabf

AUTHOR

Christian Stump, Nov 01 2015

STATUS

approved

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Last modified December 13 08:08 EST 2019. Contains 329968 sequences. (Running on oeis4.)