A319913 Number of distinct integer partitions whose parts can be combined together using additions and multiplications to obtain n, with the exception that 1's can only be added and not multiplied with other parts.

1, 2, 3, 5, 7, 16, 20, 37, 53, 81, 107, 177, 227, 332, 449, 647, 830, 1162, 1480, 2032, 2597, 3447, 4348, 5775, 7251, 9374, 11758, 15026, 18640, 23688, 29220, 36771, 45128, 56168, 68674, 85015, 103394, 126923, 153871, 187911, 226653

Offset

1,2

Comments

All parts of the integer partition must be used in such a combination.

Links

Charlie Neder, Table of n, a(n) for n = 1..46

Formula

a(n) >= A000041(n).

a(n) >= A001055(n).

Example

The a(7) = 20 partitions (which are not all partitions of 7):
  (7),
  (61), (52), (43),
  (511), (321), (421), (331), (322),
  (3111), (4111), (2211), (3211), (2221),
  (21111), (31111), (22111),
  (111111), (211111),
  (1111111).
This list contains (2211) because we can write 7 = (2+1)*2+1. It contains (321) because we can write 7 = 3*2+1, even though the sum of parts is only 6.

Crossrefs

Cf. A000792, A001970, A005520, A048249, A066739, A066815, A275870, A319850, A318949, A319909, A319910, A319912, A319925.

Sequence in context: A363720 A024377 A025069 * A073436 A094575 A145968

Adjacent sequences: A319910 A319911 A319912 * A319914 A319915 A319916

Keyword

nonn

Author

Gus Wiseman, Oct 01 2018

Extensions

a(13)-a(41) from Charlie Neder, Jun 02 2019

Status

approved