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A shell model of partitions. Triangle read by rows: row n lists the parts of the last section of the set of partitions of n.
7

%I #13 May 22 2020 13:11:26

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

%T 1,7,5,2,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,8,6,2,5,3,4,4,4,2,2,3,3,2,2,

%U 2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,7,2,6,3,5,4,5,2,2,4,3,2,3,3,3,3,2,2

%N A shell model of partitions. Triangle read by rows: row n lists the parts of the last section of the set of partitions of n.

%C Row n lists the terms of row n of A138138, in decreasing order. See the integrated diagram of partitions and more information in the entry A138138.

%H Robert Price, <a href="/A138151/b138151.txt">Table of n, a(n) for n = 1..4630, 20 rows.</a>

%e Triangle begins:

%e 1

%e 2,1

%e 3,1,1

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

%e 5,3,2,1,1,1,1,1,

%e 6,4,2,3,3,2,2,2,1,1,1,1,1,1,1

%e 7,5,2,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1

%e 8,6,2,5,3,4,4,4,2,2,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%e 9,7,2,6,3,5,4,5,2,2,4,3,2,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%t Table[Cases[IntegerPartitions[n], x_ /; Last[x] != 1] ~Join~ConstantArray[{1}, PartitionsP[n - 1]], {n, 8}] // Flatten (* _Robert Price_, May 22 2020 *)

%Y Cf. A135010, A138121, A138122, A138123, A138136, A138137, A138138, A138152, A138153.

%K nonn,tabf,less

%O 1,2

%A _Omar E. Pol_, Mar 21 2008