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A264035 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 partitions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral.

%I A264035 #11 Nov 25 2015 21:34:25
%S A264035 1,1,2,3,5,5,2,6,4,1,7,2,3,2,1,8,2,3,2,3,3,0,1
%N A264035 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 partitions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral.
%C A264035 Row sums give A000041.
%H A264035 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000205">Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight</a>.
%H A264035 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 A264035 Triangle begins:
%e A264035 1,
%e A264035 1,
%e A264035 2,
%e A264035 3,
%e A264035 5,
%e A264035 5,2,
%e A264035 6,4,1,
%e A264035 7,2,3,2,1,
%e A264035 8,2,3,2,3,3,0,1,
%e A264035 ...
%Y A264035 Cf. A000041, A264047, A264048, A264049.
%K A264035 nonn,tabf,more
%O A264035 0,3
%A A264035 _Christian Stump_, Nov 01 2015