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%I #15 Mar 30 2012 17:34:05
%S 0,0,0,0,2,3,2,2,4,3,3,2,5,4,2,2,4,3,2,2,3,6,5,4,3,2,5,4,2,2,3,7,3,3,
%T 6,5,2,2,4,3,2,2,3,6,5,4,2,2,2,2,3,4,8,4,3,7,6,5,3,2,5,4,2,2,3,7,3,3,
%U 6,5,2,2,2,2,3,3,4,9,5,4,3,4,8,7,6
%N Irregular triangle read by rows in which row n lists the emergent parts of all partitions of n, or 0 if such parts do not exist.
%C For the definition of "emergent part" see A182699 and also A182709. Also [0, 0, 0, 0] followed by the positive integers of the rows that contain zeros in the triangle A186114. For another version see A183152.
%e If written as a triangle:
%e 0,
%e 0,
%e 0,
%e 0,
%e 2,
%e 3,
%e 2,2,4,3,
%e 3,2,5,4,
%e 2,2,4,3,2,2,3,6,5,4,
%e 3,2,5,4,2,2,3,7,3,3,6,5,
%e 2,2,4,3,2,2,3,6,5,4,2,2,2,2,3,4,8,4,3,7,6,5,
%e 3,2,5,4,2,2,3,7,3,3,6,5,2,2,2,2,3,3,4,9,5,4,3,4,8,7,6
%Y Row n has length A182699(n). Row sums give A182709.
%Y Cf. A135010, A138121.
%K nonn,tabf
%O 0,5
%A _Omar E. Pol_, Aug 12 2011
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