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%I #9 Nov 25 2015 21:34:39
%S 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,
%T 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,
%U 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1
%N 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.
%C Row sums give A000041.
%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000206">Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition 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,
%e 2,
%e 3,
%e 5,
%e 5,2,
%e 6,3,0,1,0,0,1,
%e 7,1,0,0,0,0,0,2,2,0,0,1,0,0,0,0,1,1,
%e 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,
%e ...
%Y Cf. A000041, A264035, A264048, A264049.
%K nonn,tabf
%O 0,3
%A _Christian Stump_, Nov 01 2015
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