OFFSET
0,5
COMMENTS
In other words, the parts are disjoint from the first differences.
EXAMPLE
The strict partition y = (9,5,3,1) has differences (4,2,2), and these are disjoint from the parts, so y is counted under a(18).
The a(1) = 1 through a(9) = 6 strict partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(3,1) (3,2) (5,1) (4,3) (5,3) (5,4)
(4,1) (5,2) (6,2) (7,2)
(6,1) (7,1) (8,1)
(4,3,2)
(5,3,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, -Differences[#]]=={}&]], {n, 0, 15}]
PROG
(Python)
from collections import Counter
from sympy.utilities.iterables import partitions
def A364464(n): return sum(1 for s, p in map(lambda x: (x[0], tuple(sorted(Counter(x[1]).elements()))), filter(lambda p:max(p[1].values(), default=1)==1, partitions(n, size=True))) if set(p).isdisjoint({p[i+1]-p[i] for i in range(s-1)})) # Chai Wah Wu, Sep 26 2023
CROSSREFS
The non-strict version is A363260.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 30 2023
STATUS
approved