OFFSET
0,4
COMMENTS
Also the number of integer partitions of n with no two possibly equal parts summing to n.
FORMULA
EXAMPLE
The a(1) = 1 through a(8) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(111) (1111) (221) (222) (322) (332)
(311) (411) (331) (521)
(2111) (2211) (421) (611)
(11111) (21111) (511) (2222)
(111111) (2221) (3221)
(3211) (3311)
(4111) (5111)
(22111) (22211)
(31111) (32111)
(211111) (221111)
(1111111) (311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]!=2&&FreeQ[#, n/2]&]], {n, 0, 15}]
PROG
(Python)
from sympy import npartitions
def A365825(n): return npartitions(n)-(m:=n>>1)-(0 if n&1 else npartitions(m)-1) # Chai Wah Wu, Sep 23 2023
CROSSREFS
The complement is counted by A238628.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2023
EXTENSIONS
a(31)-a(47) from Chai Wah Wu, Sep 23 2023
STATUS
approved