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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. 3

%I

%S 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,

%T 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

%N 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.

%C Row sums give A000041, n >= 1.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000208">Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight</a>.

%H J. De Loera and T. B. McAllister, <a href="http://arxiv.org/abs/math/0309329">Vertices of Gelfand-Tsetlin polytopes</a>, arXiv:math/0309329 [math.CO], 2003, MathSciNet:2096742.

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,1,1,

%e 1,1,1,1,1,

%e 1,2,0,2,0,1,1,

%e 1,2,1,2,0,1,1,1,0,1,1,

%e 1,3,0,2,2,1,1,1,0,0,1,1,0,1,1,

%e 1,3,2,2,2,0,2,0,3,0,0,2,0,0,1,0,1,0,1,0,1,1,

%e ...

%Y Cf. A000041, A264035, A264047, A264048.

%K nonn,tabf

%O 1,13

%A _Christian Stump_, Nov 02 2015

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Last modified August 25 03:10 EDT 2019. Contains 326318 sequences. (Running on oeis4.)