A176207 Permutations of partitions listed in A080577 with partition lengths listed in A176208; the table has shape A058884.

1, 2, 1, 3, 1, 2, 1, 2, 3, 1, 4, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 4, 2, 3, 1, 1, 5, 1, 4, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 3, 4, 2, 5, 2, 4, 1, 2, 3, 2, 2, 3, 1, 1, 1, 6, 1, 5, 1, 1, 4, 2, 1, 4, 1, 1, 1, 3, 3, 1, 3, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1

Offset: 3

Author

Alford Arnold, Apr 12 2010

Keywords

• nonn
• tabf
• uned

Comments

The permutations are selected by considering partial sums of A080577:

1

1 2 11

1 2 11 3 21 111

...

then prepending values from A176206 yielding

1

2 11

3 21 12 111

4 31 22 211 13 121 1111

...

Cases appearing in A080577 are excluded from {a(n)}.

Examples

			Triangle begins:
  {{1,2}},
  {{1,3}, {1,2,1}},
  {{2,3}, {1 4}, {1,3,1}, {1,2,2}, {1,2,1,1}},
Or more concisely:
  {12},
  {13, 121},
  {23, 14, 131, 122, 1211},
  {24, 231, 15, 141, 132, 1311, 1221, 12111},
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..1607 (rows 3..12)

Crossrefs

Cf. A058884, A080577, A176206, A176208.

Programs

PARI

\\ here R(n) returns n-th row as vector of vectors.
L(n,k)={vecsort([Vecrev(p) | p<-partitions(k), p[#p] > n-k], , 4)}
R(n)={ concat(vector(n-1, k, [concat([n-k],p) | p<-L(n,k)])) }
{ for(n=3, 6, print(concat(R(n)))) } \\ Andrew Howroyd, Apr 21 2023

Extensions

Offset corrected and a(50) and beyond from Andrew Howroyd, Apr 21 2023