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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..79.

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

Cf. A000009, A000041, A118457, A035399.

Sequence in context: A030718 A227779 A194066 * A353171 A182628 A331366

Adjacent sequences:  A308913 A308914 A308915 * A308917 A308918 A308919

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Jun 30 2019

STATUS

approved

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Last modified June 27 10:04 EDT 2022. Contains 354896 sequences. (Running on oeis4.)