login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118457 Table of partitions of n into distinct parts, in Mathematica ordering. 11
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 (list; graph; refs; listen; history; text; internal format)
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: A280047 A106377 A214573 * A319247 A129773 A105789

Adjacent sequences:  A118454 A118455 A118456 * A118458 A118459 A118460

KEYWORD

nonn,look,tabf

AUTHOR

Franklin T. Adams-Watters, Apr 28 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 06:28 EST 2021. Contains 340266 sequences. (Running on oeis4.)