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

%I A118457 #24 Apr 11 2020 06:24:01
%S A118457 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,
%T A118457 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,
%U A118457 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
%N A118457 Table of partitions of n into distinct parts, in Mathematica ordering.
%C A118457 Reverse lexicographic order where the partitions are reprepresented as (weakly) decreasing lists of parts. [_Joerg Arndt_, Jan 25 2013]
%H A118457 Alois P. Heinz, <a href="/A118457/b118457.txt">Rows n = 1..32, flattened</a>
%e A118457 The partitions of 5 into distinct parts are [5], [4,1] and [3,2], so row 5 is 5,4,1,3,2.
%e A118457 1;
%e A118457 2;
%e A118457 3; 2,1;
%e A118457 4; 3,1;
%e A118457 5; 4,1; 3,2;
%e A118457 6; 5,1; 4,2; 3,2,1;
%e A118457 7; 6,1; 5,2; 4,3; 4,2,1;
%e A118457 8; 7,1; 6,2; 5,3; 5,2,1; 4,3,1;
%e A118457 9; 8,1; 7,2; 6,3; 6,2,1; 5,4; 5,3,1; 4,3,2;
%e A118457 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;
%e A118457 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;
%t A118457 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@ #] == 1 &]; Flatten[Table[d[n], {n, 15}]] (* _Clark Kimberling_, Mar 11 2012 *)
%o A118457 (SageMath)
%o A118457 def StrictPartitions(n): return [partition for partition in Partitions(n) if Set(partition.to_exp()).issubset(Set([0,1]))]
%o A118457 def A118457row(n): return [p for parts in StrictPartitions(n) for p in parts]
%o A118457 for n in (1..9): print(A118457row(n)) # _Peter Luschny_, Apr 11 2020
%Y A118457 Cf. A026793, A118459 (partition lengths), A015723 (total row lengths), A080577, A000009, A246688.
%K A118457 nonn,look,tabf
%O A118457 1,2
%A A118457 _Franklin T. Adams-Watters_, Apr 28 2006