cp's OEIS Frontend

A211025 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.

%I A211025 #18 Dec 01 2013 13:36:34
%S A211025 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 A211025 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 A211025 5,6,7,8,9,10,11,12,13,14,15,17,19,21,23,25,27
%N A211025 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 A211025 Also triangle read by rows in which row n lists the partial sums of row n of triangle A135010.
%C A211025 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 A211025 For row n = 5 of triangle we have:
%e A211025 -------------------------------------
%e A211025 Column  Zone    The 5th    Total sum
%e A211025 k                shell     of parts
%e A211025 -------------------------------------
%e A211025 8    <>   7       (5)         15
%e A211025 7    <>   6    (3...          10
%e A211025 6    =    6     ...2)          7
%e A211025 5    =    5       (1)          5
%e A211025 4    =    4       (1)          4
%e A211025 3    =    3       (1)          3
%e A211025 2    =    2       (1)          2
%e A211025 1    =    1       (1)          1
%e A211025 .
%e A211025 Triangle begins:
%e A211025 1;
%e A211025 1,3;
%e A211025 1,2,5;
%e A211025 1,2,3,5,7,11;
%e A211025 1,2,3,4,5,7,10,15;
%e A211025 1,2,3,4,5,6,7,9,11,13,15,19,22,25,31;
%e A211025 1,2,3,4,5,6,7,8,9,10,11,13,15,18,20,25,28,32,39;
%Y A211025 Row n has length A138137(n). Right border gives A138879.
%Y A211025 Cf. A135010, A182703, A206437, A211030.
%K A211025 nonn,tabf
%O A211025 1,3
%A A211025 _Omar E. Pol_, Apr 25 2012