A339351 - OEIS

%I #4 Dec 01 2020 17:07:15

%S 1,2,1,2,2,1,3,1,3,3,1,4,1,4,2,3,3,2,4,1,5,1,2,3,1,3,2,1,5,2,1,3,2,3,

%T 1,2,4,3,1,2,3,2,1,4,2,5,1,6,1,2,4,1,4,2,1,6,2,1,4,2,4,1,2,5,3,4,4,1,

%U 2,4,2,1,4,3,5,2,6,1,7,1,2,5,1,3,4,1,4,3,1,5,2,1,7,2,1,5,2,5,1,2,6,3,1,4,3,4,1,3,5,4,1,3,4,3,1,5,1,2,5,2,1,5,3,6,2,7,1,8

%N Irregular triangle read by rows in which row n lists the compositions (ordered partitions) of n into distinct parts in lexicographic order.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%e Triangle begins:

%e [1],

%e [2],

%e [1, 2], [2, 1], [3],

%e [1, 3], [3, 1], [4],

%e [1, 4], [2, 3], [3, 2], [4, 1], [5],

%e ...

%t Table[Sort[Join @@ Permutations /@ Select[IntegerPartitions[n], UnsameQ @@ # &], OrderedQ[PadRight[{#1, #2}]] &], {n, 8}] // Flatten

%Y Cf. A026793, A066099, A097910 (row lengths), A118457, A228369, A246688, A304797 (row sums), A339178.

%K nonn,tabf

%O 1,2

%A _Ilya Gutkovskiy_, Dec 01 2020