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A319910 Number of distinct pairs (m, y), where m >= 1 and y is an integer partition of n, such that m can be obtained by iteratively adding or multiplying together parts of y until only one part (equal to m) remains. 9
1, 3, 6, 11, 23, 48, 85, 178, 331, 619, 1176, 2183, 3876, 7013, 12447, 21719, 37628, 64570, 109723, 185055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

The a(4) = 11 pairs:

  4 <= (4)

  3 <= (3,1)

  4 <= (3,1)

  4 <= (2,2)

  2 <= (2,1,1)

  3 <= (2,1,1)

  4 <= (2,1,1)

  1 <= (1,1,1,1)

  2 <= (1,1,1,1)

  3 <= (1,1,1,1)

  4 <= (1,1,1,1)

MATHEMATICA

ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]];

nexos[ptn_]:=If[Length[ptn]==0, {0}, Union@@Select[ReplaceListRepeated[{Sort[ptn]}, {{foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x+y]], {foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]];

Table[Total[Length/@nexos/@IntegerPartitions[n]], {n, 20}]

CROSSREFS

Cf. A000792, A001970, A005520, A048249, A066739, A066815, A275870, A319850, A318949, A319909, A319912, A319913.

Sequence in context: A088052 A045693 A051284 * A319636 A001867 A000998

Adjacent sequences:  A319907 A319908 A319909 * A319911 A319912 A319913

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 01 2018

STATUS

approved

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Last modified November 20 05:07 EST 2019. Contains 329323 sequences. (Running on oeis4.)