A327702 Number of refinement sequences n -> ... -> {1}^n, where in each step one part that is the rightmost copy of its size is replaced by a partition of itself into smaller parts (in weakly decreasing order).

1, 1, 2, 5, 14, 47, 174, 730, 3300, 16361, 85991, 485982, 2877194, 18064663, 118111993, 810388956, 5755059363, 42643884970, 325468477721, 2576976440845, 20960795772211, 176056148076418, 1514733658531058, 13418942409623726, 121442280888373117, 1128425823360525506

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..58

Wikipedia, Partition (number theory)

Example

a(4) = 5:
  4 -> 1111
  4 -> 211  -> 1111
  4 -> 31   -> 1111
  4 -> 31   -> 211  -> 1111
  4 -> 22   -> 211  -> 1111

Maple

v:= l-> [seq(`if`(i=1 or l[i]>l[i-1], seq(subs(1=[][], sort(
         subsop(i=h[], l))), h=({combinat[partition](l[i])[]}
         minus{[l[i]]})), [][]), i=1..nops(l))]:
b:= proc(l) option remember; `if`(max(l)<2, 1, add(b(h), h=v(l))) end:
a:= n-> b([n]):
seq(a(n), n=1..26);

Crossrefs

Cf. A002846, A327643, A327697, A327698, A327699.

Sequence in context: A287888 A115276 A343664 * A317784 A096402 A007268

Adjacent sequences: A327699 A327700 A327701 * A327703 A327704 A327705

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2019

Status

approved