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%I #7 Mar 12 2022 13:14:19
%S 3,5,2,7,4,3,2,2,9,5,4,6,3,3,3,3,2,2,2,2,11,6,5,7,4,8,3,4,4,3,5,3,3,2,
%T 2,2,2,2,2,2,2,13,7,6,8,5,9,4,5,4,4,10,3,5,5,3,6,4,3,7,3,3,4,3,3,3,2,
%U 2,2,2,2,2,2,2,2,2,2,2,2,2
%N Triangle read by rows in which row n lists the parts of the largest subshell of all partitions of 2n+1 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+1 contains n subshells.
%C The first n rows of this triangle represent these subsells.
%C This sequence contains the same elements of A182743 but in distinct order.
%C See A135010 and A138121 for more information.
%e For n=1 the unique partition of 2n+1=3 that does not contains 1 as part is 3, so row 1 has an element = 3.
%e For n=2 there are 2 partitions of 2n+1=5 that do not contain 1 as part:
%e 5 ............ or ....... 5 . . . .
%e 3 + 2 ........ or .......(3). . 2 .
%e These partitions contain (3), the row n-1 of triangle, so
%e the parts of the largest subshell are 5, 2.
%e For n=3 there are 4 partitions of 2n+1=7 that do not contain 1 as part:
%e 7 ............ or ....... 7 . . . . . .
%e 4 + 3 ........ or ....... 4 . . . 3 . .
%e 5 + 2 ........ or .......(5). . . . 2 .
%e 3 + 2 + 2 .... or .......(3). .(2). 2 .
%e These partitions contain (5) and (3),(2), the parts of the rows < n of triangle, so the parts of the largest subshell are 7, 4, 3, 2, 2.
%e And so on.
%e Triangle begins:
%e 3,
%e 5,2,
%e 7,4,3,2,2,
%e 9,5,4,6,3,3,3,3,2,2,2,2,
%e 11,6,5,7,4,8,3,4,4,3,5,3,3,2,2,2,2,2,2,2,2,
%Y Cf. A135010, A138121, A182735, A182737, A182743, A182747, A182812.
%K nonn,tabf
%O 1,1
%A _Omar E. Pol_, Dec 04 2010
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