

A329255


Irregular triangle read by rows: T(n,k) is greatest positive integer <= n that have a partition into k consecutive parts, 1 <= k <= A003056(n), n >= 1.


0



1, 2, 3, 3, 4, 3, 5, 5, 6, 5, 6, 7, 7, 6, 8, 7, 6, 9, 9, 9, 10, 9, 9, 10, 11, 11, 9, 10, 12, 11, 12, 10, 13, 13, 12, 10, 14, 13, 12, 14, 15, 15, 15, 14, 15, 16, 15, 15, 14, 15, 17, 17, 15, 14, 15, 18, 17, 18, 18, 15, 19, 19, 18, 18, 15, 20, 19, 18, 18, 20, 21, 21, 21, 18, 20, 21, 22, 21, 21, 22, 20, 21
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OFFSET

1,2


COMMENTS

T(n,k) is also the positive integer whose partition into k consecutive parts is associated to the kth vertex, from left to right, of the largest Dyck path of the symmetric representation of sigma(n). For more information see A237593.
Also this triangle can be constructed replacing every zero of triangle A285891 with the previous positive integer from the same column.


LINKS



EXAMPLE

Triangle begins:
1;
2;
3, 3;
4, 3;
5, 5;
6, 5, 6;
7, 7, 6;
8, 7, 6;
9, 9, 9;
10, 9, 9, 10;
11, 11, 9, 10;
12, 11, 12, 10;
13, 13, 12, 10;
14, 13, 12, 14;
15, 15, 15, 14, 15;
16, 15, 15, 14, 15;
17, 17, 15, 14, 15;
18, 17, 18, 18, 15;
19, 19, 18, 18, 15;
20, 19, 18, 18, 20;
21, 21, 21, 18, 20, 21;
22, 21, 21, 22, 20, 21;
23, 23, 21, 22, 20, 21;
24, 23, 24, 22, 20, 21;
25, 25, 24, 22, 25, 21;
26, 25, 24, 26, 25, 21;
27, 27, 27, 26, 25, 27;
28, 27, 27, 26, 25, 27, 28;
...


CROSSREFS

Cf. A196020, A204217, A211343, A235791, A236104, A235791, A237048, A237591, A237593, A285900, A285914, A285891, A286000, A286001, A286013, A299765, A328361, A328365, A328371.


KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



