cp's OEIS Frontend

A182715 Triangle read by rows in which row n lists in nonincreasing order the smallest part of every partition of n.

%I A182715 #26 Dec 28 2023 09:25:21
%S A182715 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 A182715 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 A182715 4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1
%N A182715 Triangle read by rows in which row n lists in nonincreasing order the smallest part of every partition of n.
%C A182715 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 A182715 Also, row n lists the "filler parts" of all partition of n. For more information see A182699.
%C A182715 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 A182715 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 A182715 For row 10, see the illustration of the link.
%e A182715 Triangle begins:
%e A182715   0,
%e A182715   1,
%e A182715   2,1,
%e A182715   3,1,1,
%e A182715   4,2,1,1,1,
%e A182715   5,2,1,1,1,1,1,
%e A182715   6,3,2,2,1,1,1,1,1,1,1,
%e A182715   7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,
%e A182715   8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%e A182715   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 A182715   ...
%Y A182715 Cf. A026807, A135010, A138121, A141285, A182699, A182709.
%Y A182715 Mirror of triangle A196931.
%K A182715 nonn,tabf
%O A182715 0,3
%A A182715 _Omar E. Pol_, Dec 01 2010
%E A182715 Name simplified and more terms from _Omar E. Pol_, Oct 21 2011