%I #31 Dec 28 2023 09:25:31

%S 0,1,1,2,1,1,3,1,1,1,2,4,1,1,1,1,1,2,5,1,1,1,1,1,1,1,2,2,3,6,1,1,1,1,

%T 1,1,1,1,1,1,1,2,2,3,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,8,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Triangle read by rows in which row n lists in nondecreasing order the smallest part of every partition of n.

%C If n >= 1, row n lists the smallest parts of every partition of n in the order produced by the shell model of partitions of A135010, hence row n lists the parts of the last section of the set of partitions of n, except the emergent parts (See A182699).

%C Row n has length A000041(n). Row sums give A046746. Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.

%e Written as a triangle:

%e 0,

%e 1,

%e 1,2,

%e 1,1,3,

%e 1,1,1,2,4,

%e 1,1,1,1,1,2,5,

%e 1,1,1,1,1,1,1,2,2,3,6

%e 1,1,1,1,1,1,1,1,1,1,1,2,2,3,7,

%e 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,8,

%e ...

%Y Mirror of triangle A182715.

%Y Cf. A000041, A046746, A135010, A138121, A141285, A182699, A183152, A193827, A196930.

%K nonn,tabf

%O 0,4

%A _Omar E. Pol_, Oct 21 2011