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%I #26 Dec 28 2023 09:25:21
%S 0,1,2,1,3,1,1,4,2,1,1,1,5,2,1,1,1,1,1,6,3,2,2,1,1,1,1,1,1,1,7,3,2,2,
%T 1,1,1,1,1,1,1,1,1,1,1,8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,
%U 4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1
%N Triangle read by rows in which row n lists in nonincreasing order the smallest part of every partition of n.
%C Triangle read by rows in which row n lists the smallest parts of all partitions of n in the order produced by the shell model of partitions of A138121.
%C Also, row n lists the "filler parts" of all partition of n. For more information see A182699.
%C Row n has length A000041(n). Row sums give A046746. Column 1 gives A001477. The last A000041(n-1) terms of row n are ones, n >= 1.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpanxt.jpg">Illustration of the smallest parts of all partitions of 10 (colored blue) in the shell model of partitions</a>
%e For row 10, see the illustration of the link.
%e Triangle begins:
%e 0,
%e 1,
%e 2,1,
%e 3,1,1,
%e 4,2,1,1,1,
%e 5,2,1,1,1,1,1,
%e 6,3,2,2,1,1,1,1,1,1,1,
%e 7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,
%e 8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%e 9,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%e ...
%Y Cf. A026807, A135010, A138121, A141285, A182699, A182709.
%Y Mirror of triangle A196931.
%K nonn,tabf
%O 0,3
%A _Omar E. Pol_, Dec 01 2010
%E Name simplified and more terms from _Omar E. Pol_, Oct 21 2011
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