OFFSET
1,5
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..95
EXAMPLE
The partition y = (3,3,2) has distinct parts {2,3}, and we have 9 = 3*2 + 1*3, so y is not counted under a(9).
The a(3) = 1 through a(10) = 16 partitions:
(2) (3) (2) (4) (2) (3) (2) (3)
(3) (5) (3) (5) (4) (4)
(4) (3,2) (4) (6) (5) (6)
(2,2) (5) (7) (6) (7)
(6) (3,3) (7) (8)
(2,2) (4,3) (8) (9)
(3,3) (5,2) (2,2) (3,3)
(4,2) (4,2) (4,4)
(2,2,2) (4,3) (5,2)
(4,4) (5,3)
(5,3) (5,4)
(6,2) (6,3)
(2,2,2) (7,2)
(4,2,2) (3,3,3)
(2,2,2,2) (4,3,2)
(5,2,2)
MATHEMATICA
combp[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 1, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Table[Length[Select[Join@@IntegerPartitions/@Range[n-1], combp[n, Union[#]]=={}&]], {n, 10}]
PROG
(Python)
from sympy.utilities.iterables import partitions
def A365323(n):
a = {tuple(sorted(set(p))) for p in partitions(n)}
return sum(1 for k in range(1, n) for d in partitions(k) if tuple(sorted(set(d))) not in a) # Chai Wah Wu, Sep 12 2023
CROSSREFS
For length-2 subsets we have A365321 (we use n instead of n-1).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2023
EXTENSIONS
a(21)-a(51) from Chai Wah Wu, Sep 12 2023
STATUS
approved