A327699 Number of refinement sequences n -> ... -> {1}^n, where in each step every single part of a nonempty selection of parts is replaced by a partition of itself into two smaller parts (in weakly decreasing order).

1, 1, 1, 4, 9, 48, 211, 1736, 9777, 91169, 739174, 8613817, 83763730, 1105436491, 13222076337, 207852246589, 2789691577561, 47759515531854, 755158220565169, 14595210284816038, 255814560447492788, 5373613110108953192, 105867623217924984398, 2460702471446564481641

Offset

1,4

Links

Table of n, a(n) for n=1..24.

Wikipedia, Partition (number theory)

Example

a(4) = 4:
  4 -> 31   -> 211  -> 1111
  4 -> 22   -> 1111
  4 -> 22   -> 112  -> 1111
  4 -> 22   -> 211  -> 1111

Crossrefs

Cf. A002846, A327643, A327697, A327698, A327702.

Sequence in context: A298986 A103933 A256880 * A013495 A164839 A225885

Adjacent sequences: A327696 A327697 A327698 * A327700 A327701 A327702

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2019

Status

approved