A246688 Triangle in which n-th row lists lexicographically ordered increasing lists of parts of all partitions of n into distinct parts.

1, 2, 1, 2, 3, 1, 3, 4, 1, 4, 2, 3, 5, 1, 2, 3, 1, 5, 2, 4, 6, 1, 2, 4, 1, 6, 2, 5, 3, 4, 7, 1, 2, 5, 1, 3, 4, 1, 7, 2, 6, 3, 5, 8, 1, 2, 6, 1, 3, 5, 1, 8, 2, 3, 4, 2, 7, 3, 6, 4, 5, 9, 1, 2, 3, 4, 1, 2, 7, 1, 3, 6, 1, 4, 5, 1, 9, 2, 3, 5, 2, 8, 3, 7, 4, 6, 10

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..32, flattened

Example

Triangle begins:
  [1];
  [2];
  [1,2], [3];
  [1,3], [4];
  [1,4], [2,3], [5];
  [1,2,3], [1,5], [2,4], [6];
  [1,2,4], [1,6], [2,5], [3,4], [7];
  [1,2,5], [1,3,4], [1,7], [2,6], [3,5], [8];
  [1,2,6], [1,3,5], [1,8], [2,3,4], [2,7], [3,6], [4,5], [9];
  [1,2,3,4], [1,2,7], [1,3,6], [1,4,5], [1,9], [2,3,5], [2,8], [3,7], [4,6], [10];

Maple

b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],
      [map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))
    end:
T:= n-> map(x-> x[], b(n, 1))[]:
seq(T(n), n=1..12);

Mathematica

T[n_] := Module[{ip, lg}, ip = Reverse /@ Select[ IntegerPartitions[n], # == DeleteDuplicates[#]&]; lg = Length /@ ip // Max; SortBy[PadRight[#, lg]&][ip]];
Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Oct 21 2022 *)

Crossrefs

Row lengths are A015723.

Row sums give A066189.

Last elements of rows are A000027.

Cf. A026791, A026793, A118457, A265146.

Sequence in context: A358136 A325537 A072851 * A103627 A344088 A292595

Adjacent sequences: A246685 A246686 A246687 * A246689 A246690 A246691

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 01 2014

Status

approved