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

3,1

Links

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

Example

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;
  ...

Prog

(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

Crossrefs

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

Sequence in context: A237769 A187182 A362816 * A330623 A153095 A254574

Adjacent sequences: A176205 A176206 A176207 * A176209 A176210 A176211

Keyword

nonn,tabf,uned

Author

Alford Arnold, Apr 12 2010

Extensions

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

Status

approved