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.

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

Offset

1,3

Comments

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

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.

Links

Table of n, a(n) for n=1..75.

Example

For row n = 5 of triangle we have:
-------------------------------------
Column  Zone    The 5th    Total sum
k                shell     of parts
-------------------------------------
8    <>   7       (5)         15
7    <>   6    (3...          10
6    =    6     ...2)          7
5    =    5       (1)          5
4    =    4       (1)          4
3    =    3       (1)          3
2    =    2       (1)          2
1    =    1       (1)          1
.
Triangle begins:
1;
1,3;
1,2,5;
1,2,3,5,7,11;
1,2,3,4,5,7,10,15;
1,2,3,4,5,6,7,9,11,13,15,19,22,25,31;
1,2,3,4,5,6,7,8,9,10,11,13,15,18,20,25,28,32,39;

Crossrefs

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

Cf. A135010, A182703, A206437, A211030.

Sequence in context: A123375 A021036 A354348 * A125704 A357498 A131127

Adjacent sequences: A211022 A211023 A211024 * A211026 A211027 A211028

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 25 2012

Status

approved