A308916 - OEIS

%I #8 Jul 03 2019 04:08:20

%S 1,1,1,2,1,2,1,2,3,1,2,3,6,1,2,3,5,6,1,2,3,5,6,9,1,2,3,5,6,8,9,14,1,2,

%T 3,5,6,8,9,14,15,23,1,2,3,5,6,8,9,13,14,15,21,24,1,2,3,5,6,8,9,13,14,

%U 15,21,22,25,33,34,1,2,3,5,6,8,9,13,14,15

%N Irregular triangular array: row n shows positions of strict partitions of n among all partitions of n, using Mathematica ordering.

%e 1

%e 1

%e 1   2

%e 1   2

%e 1   2   3

%e 1   2   3   6

%e 1   2   3   5   6

%e 1   2   3   5   6   9

%e 1   2   3   5   6   8   9   14

%e 1   2   3   5   6   8   9   14   15   23

%e Strict partitions of 6: {6}, {5, 1}, {4, 2}, {3, 2, 1}, which occupy positions 1,2,3,6 in the ordering of all partitions of 6: {6}, {5, 1}, {4, 2}, {4, 1, 1}, {3, 3}, {3, 2, 1}, {3, 1, 1, 1}, {2, 2, 2}, {2, 2, 1, 1}, {2, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}

%t p[n_] := IntegerPartitions[n];

%t d[n_] := Select[p[n], Max[Length /@ Split@#] == 1 &];

%t t = Table[Flatten[Table[Position[p[n], d[n][[k]]], {k, 1, Length[d[n]]}]], {n, 1, 15}]

%t Flatten[t]  (* A308916, sequence *)

%Y Cf. A000009, A000041, A118457, A035399.

%K nonn,tabf,easy

%O 1,4

%A _Clark Kimberling_, Jun 30 2019