OFFSET
1,3
COMMENTS
Also the finite sequence a(1)..a(r), where a(r) is a record in the sequence, is also a finite triangle read by rows: T(n,k) = number of cells in the k-column of the n-th region of the integer whose number of partitions is equal to a(r).
T(n,k) is also 1 plus the number of holes between T(n,k) and the previous member in the column k of triangle.
T(n,k) is also the height of the column mentioned in the definition, in a three-dimensional model of the set of partitions of j, in which the regions appear rotated 90 degrees and where the pivots are the largest part of every region (see A141285). For the definition of "region" see A206437. - Omar E. Pol, Feb 06 2014
LINKS
EXAMPLE
The irregular triangle begins:
1;
1, 2;
1, 1, 3;
1, 1;
1, 1, 2, 5;
1, 1, 1;
1, 1, 1, 2, 7;
1, 1;
1, 1, 2, 2;
1, 1, 1;
1, 1, 1, 2, 4, 11;
1, 1, 1;
1, 1, 1, 2, 2;
1, 1, 1, 1;
1, 1, 1, 1, 2, 4, 15;
1, 1;
1, 1, 2, 2;
1, 1, 1;
1, 1, 1, 2, 4, 4;
1, 1, 1, 1, 1;
1, 1, 1, 1;
1, 1, 1, 1, 2, 3, 7, 22;
...
From Omar E. Pol, Feb 06 2014: (Start)
Illustration of initial terms:
. _
. |_|
. 1
. _
. _|_|
. |_ _|
. 1 2
. _
. |_|
. _ _|_|
. |_ _ _|
. 1 1 3
. _ _
. |_ _|
. 1 1
. _
. |_|
. |_|
. _|_|
. _ _|_ _|
. |_ _ _ _|
. 1 1 2 5
.
(End)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Oct 21 2012
EXTENSIONS
Better definition from Omar E. Pol, Feb 06 2014
STATUS
approved