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

3,2

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)}.

Links

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

Example

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},
  ...

Prog

(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

Crossrefs

Cf. A058884, A080577, A176206, A176208.

Sequence in context: A184166 A029423 A184169 * A059130 A094959 A162696

Adjacent sequences: A176204 A176205 A176206 * A176208 A176209 A176210

Keyword

nonn,tabf,uned

Author

Alford Arnold, Apr 12 2010

Extensions

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

Status

approved