A176208 An irregular table with shape sequence A058884 measuring the length of ordered partitions defined by A176207.

2, 2, 3, 2, 2, 3, 3, 4, 2, 3, 2, 3, 3, 4, 4, 5, 2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 2, 3, 2, 3, 3, 4, 3, 4, 5, 2, 3, 3, 4, 3, 4, 5, 4, 4, 5, 6, 5, 6, 7, 2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 5, 4, 4, 5, 6, 2, 3, 3, 4, 3, 4, 5, 3, 4, 4, 5, 6, 4, 5, 5, 6, 7, 5, 6, 7, 8

Offset: 3

Author

Alford Arnold, Apr 12 2010

Keywords

• nonn
• tabf
• uned

Examples

			A058884 begins -1 0 0 1 2 5 8 15 ..., counting
  12
  13 121
  23 14 131 122 1211
  ...
so triangle T(n,k) begins:
  2;
  2, 3;
  2, 2, 3, 3, 4;
  2, 3, 2, 3, 3, 4, 4, 5;
  2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 5, 4, 5, 6;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..5555 (rows 3..20)

Crossrefs

Cf. A058884 (row lengths), A176206, A176207.

Programs

PARI

L(n,k)={vecsort([Vecrev(p) | p<-partitions(k), p[#p] > n-k], , 4)}
row(n)={ concat(vector(n-1, k, [#p + 1 | p<-L(n,k)])) }
for(n=3, 8, print(row(n))) \\ Andrew Howroyd, Apr 21 2023

Extensions

Terms a(34) and beyond from Andrew Howroyd, Apr 21 2023