A211025 - OEIS

%I #18 Dec 01 2013 13:36:34

%S 1,1,3,1,2,5,1,2,3,5,7,11,1,2,3,4,5,7,10,15,1,2,3,4,5,6,7,9,11,13,15,

%T 19,22,25,31,1,2,3,4,5,6,7,8,9,10,11,13,15,18,20,25,28,32,39,1,2,3,4,

%U 5,6,7,8,9,10,11,12,13,14,15,17,19,21,23,25,27

%N Triangle read by rows: T(n,k) = total sum of parts in the last section of the set of partitions of n after k-th stage.

%C Also triangle read by rows in which row n lists the partial sums of row n of triangle A135010.

%C This triangle shows the growth of the last sections of the partitions of n step by step. At stage k one part of size A135010(n,k) is added to the structure of the n-th shell.

%e For row n = 5 of triangle we have:

%e -------------------------------------

%e Column  Zone    The 5th    Total sum

%e k                shell     of parts

%e -------------------------------------

%e 8    <>   7       (5)         15

%e 7    <>   6    (3...          10

%e 6    =    6     ...2)          7

%e 5    =    5       (1)          5

%e 4    =    4       (1)          4

%e 3    =    3       (1)          3

%e 2    =    2       (1)          2

%e 1    =    1       (1)          1

%e .

%e Triangle begins:

%e 1;

%e 1,3;

%e 1,2,5;

%e 1,2,3,5,7,11;

%e 1,2,3,4,5,7,10,15;

%e 1,2,3,4,5,6,7,9,11,13,15,19,22,25,31;

%e 1,2,3,4,5,6,7,8,9,10,11,13,15,18,20,25,28,32,39;

%Y Row n has length A138137(n). Right border gives A138879.

%Y Cf. A135010, A182703, A206437, A211030.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, Apr 25 2012