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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.
16
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
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 01 2018
EXTENSIONS
a(13)-a(41) from Charlie Neder, Jun 02 2019
STATUS
approved