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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). 5
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 (list; graph; refs; listen; history; text; internal format)
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: A149904 A287888 A115276 * A317784 A096402 A007268

Adjacent sequences:  A327699 A327700 A327701 * A327703 A327704 A327705

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2019

STATUS

approved

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Last modified February 19 01:03 EST 2020. Contains 332028 sequences. (Running on oeis4.)