OFFSET
0,7
COMMENTS
In other words, strict partitions with parts not disjoint from first differences.
EXAMPLE
The a(3) = 1 through a(15) = 11 partitions (A = 10, B = 11, C = 12):
21 . . 42 421 431 63 532 542 84 742 743 A5
321 521 621 541 632 642 841 752 843
631 821 651 A21 761 942
721 5321 921 5431 842 C21
4321 5421 6421 B21 6432
6321 7321 6431 6531
6521 7431
7421 7521
8321 8421
9321
54321
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, -Differences[#]]!={}&]], {n, 0, 30}]
PROG
(Python)
from collections import Counter
from sympy.utilities.iterables import partitions
def A364536(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 not set(p).isdisjoint({p[i+1]-p[i] for i in range(s-1)})) # Chai Wah Wu, Sep 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 31 2023
STATUS
approved