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

1,2

Comments

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

Links

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

Example

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;

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A214573 A344090 A344092 * A319247 A343180 A129773

Adjacent sequences: A118454 A118455 A118456 * A118458 A118459 A118460

Keyword

nonn,look,tabf

Author

Franklin T. Adams-Watters, Apr 28 2006

Status

approved