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A308916
Irregular triangular array: row n shows positions of strict partitions of n among all partitions of n, using Mathematica ordering.
1
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
1,4
EXAMPLE
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}
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 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Jun 30 2019
STATUS
approved