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%I #12 Dec 01 2015 06:58:21
%S 1,0,1,0,1,1,1,1,1,1,0,1,2,1,1,0,1,2,2,1,1,1,1,2,3,2,1,1,0,1,2,3,3,2,
%T 1,1,0,1,2,3,4,3,2,1,1,1,1,2,4,4,4,3,2,1,1,0,1,2,3,5,5,4,3,2,1,1,0,1,
%U 2,3,5,6,5,4,3,2,1,1,1,1,2,4,5,6,7,5,4,3,2,1,1
%N Triangle read by rows: T(n,k) (0 <= k <= n) = number of principal ideals generated by an element of rank k in the 3-tonal partition monoid on n elements.
%H C. Ahmed, P. Martin, V. Mazorchuk, <a href="http://arxiv.org/abs/1503.06718">On the number of principal ideals in d-tonal partition monoids</a>, arXiv preprint arXiv:1503.06718 [math.CO], 2015. See Fig. 2.
%e Triangle begins:
%e 1,
%e 0,1,
%e 0,1,1,
%e 1,1,1,1,
%e 0,1,2,1,1,
%e 0,1,2,2,1,1,
%e 1,1,2,3,2,1,1,
%e 0,1,2,3,3,2,1,1,
%e 0,1,2,3,4,3,2,1,1,
%e 1,1,2,4,4,4,3,2,1,1,
%e 0,1,2,3,5,5,4,3,2,1,1,
%e 0,1,2,3,5,6,5,4,3,2,1,1,
%e 1,1,2,4,5,6,7,5,4,3,2,1,1,
%e ...
%Y Cf. A028289.
%K nonn,tabl
%O 0,13
%A _N. J. A. Sloane_, Nov 30 2015
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