A118457 Table of partitions of n into distinct parts, in Mathematica ordering.

1, 2, 3, 2, 1, 4, 3, 1, 5, 4, 1, 3, 2, 6, 5, 1, 4, 2, 3, 2, 1, 7, 6, 1, 5, 2, 4, 3, 4, 2, 1, 8, 7, 1, 6, 2, 5, 3, 5, 2, 1, 4, 3, 1, 9, 8, 1, 7, 2, 6, 3, 6, 2, 1, 5, 4, 5, 3, 1, 4, 3, 2, 10, 9, 1, 8, 2, 7, 3, 7, 2, 1, 6, 4, 6, 3, 1, 5, 4, 1, 5, 3, 2, 4, 3, 2, 1, 11, 10, 1, 9, 2, 8, 3, 8, 2, 1, 7, 4, 7, 3, 1, 6, 5

Offset: 1

Author

Franklin T. Adams-Watters, Apr 28 2006

Keywords

• nonn
• look
• tabf

Comments

Reverse lexicographic order where the partitions are reprepresented as (weakly) decreasing lists of parts. [Joerg Arndt, Jan 25 2013]

Examples

			The partitions of 5 into distinct parts are [5], [4,1] and [3,2], so row 5 is 5,4,1,3,2.
1;
2;
3; 2,1;
4; 3,1;
5; 4,1; 3,2;
6; 5,1; 4,2; 3,2,1;
7; 6,1; 5,2; 4,3; 4,2,1;
8; 7,1; 6,2; 5,3; 5,2,1; 4,3,1;
9; 8,1; 7,2; 6,3; 6,2,1; 5,4; 5,3,1; 4,3,2;
10; 9,1; 8,2; 7,3; 7,2,1; 6,4; 6,3,1; 5,4,1; 5,3,2; 4,3,2,1;
11; 10,1; 9,2; 8,3; 8,2,1; 7,4; 7,3,1; 6,5; 6,4,1; 6,3,2; 5,4,2; 5,3,2,1;
		

Links

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

Crossrefs

Cf. A026793, A118459 (partition lengths), A015723 (total row lengths), A080577, A000009, A246688.

Programs

Mathematica

d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@ #] == 1 &]; Flatten[Table[d[n], {n, 15}]] (* Clark Kimberling, Mar 11 2012 *)

SageMath

def StrictPartitions(n): return [partition for partition in Partitions(n) if Set(partition.to_exp()).issubset(Set([0,1]))]
def A118457row(n): return [p for parts in StrictPartitions(n) for p in parts]
for n in (1..9): print(A118457row(n)) # Peter Luschny, Apr 11 2020