A308916 Irregular triangular array: row n shows positions of strict partitions of n among all partitions of n, using Mathematica ordering.

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

Offset: 1

Author

Clark Kimberling, Jun 30 2019

Keywords

• nonn
• tabf
• easy

Examples

			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   3   5   6   8   9   14   15   23
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}
		

Crossrefs

Cf. A000009, A000041, A118457, A035399.

Programs

Mathematica

p[n_] := IntegerPartitions[n];
d[n_] := Select[p[n], Max[Length /@ Split@#] == 1 &];
t = Table[Flatten[Table[Position[p[n], d[n][[k]]], {k, 1, Length[d[n]]}]], {n, 1, 15}]
Flatten[t]  (* A308916, sequence *)