%I
%S 2,4,2,6,3,3,2,2,8,4,4,5,3,2,2,2,2,10,5,5,6,4,7,3,4,3,3,2,2,2,2,2,2,2,
%T 12,6,6,7,5,8,4,4,4,4,9,3,5,4,3,6,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,
%U 14,7,7,8,6,9,5
%N Triangle read by rows in which row n lists the parts of the largest subshell of all partitions of 2n that do not contain 1 as a part.
%C In the shell model of partitions the head of the last section of the set of partitions of 2n contains n subshells. The first n rows of this triangle represent these subsells.
%C This sequence contains the same elements of A182742 but in distinct order.
%C See A135010 and A138121 for more information.
%e For n=1 the unique partition of 2n that does not contains 1 as part is 2, so row 1 has an element = 2.
%e For n=2 there are 2 partitions of 2n that do not contain 1 as part:
%e 4 ............ or ....... 4 . . .
%e 2 + 2 ........ or .......(2). 2 .
%e These partitions contain (2), the row n1 of triangle, so
%e the parts of the largest subshell are 4, 2.
%e For n=3 there are 4 partitions of 2n that do not contain 1 as part:
%e 6 ............ or ....... 6 . . . . .
%e 3 + 3 ........ or ....... 3 . . 3 . .
%e 4 + 2 ........ or .......(4). . . 2 .
%e 2 + 2 + 2 .... or .......(2).(2). 2 .
%e These partitions contain (4) and (2),(2), the parts of rows < n of triangle, so the parts of the largest subshell are 6, 3, 3, 2, 2.
%e And so on.
%e Triangle begins:
%e 2,
%e 4, 2,
%e 6, 3, 3, 2, 2,
%e 8, 4, 4, 5, 3, 2, 2, 2, 2,
%e 10, 5, 5, 6, 4, 7, 3, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2,
%Y Cf. A135010, A138121, A182734, A182736, A182742, A182746, A182813.
%K nonn,tabf
%O 1,1
%A _Omar E. Pol_, Dec 04 2010
