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A361394
Number of integer partitions of n where 2*(number of distinct parts) >= (number of parts).
15
1, 1, 2, 2, 4, 6, 8, 11, 15, 20, 30, 38, 49, 65, 83, 108, 139, 178, 224, 286, 358, 437, 550, 684, 837, 1037, 1269, 1553, 1889, 2295, 2770, 3359, 4035, 4843, 5808, 6951, 8312, 9902, 11752, 13958, 16531, 19541, 23037, 27162, 31911, 37488, 43950, 51463, 60127, 70229
OFFSET
0,3
LINKS
EXAMPLE
The a(1) = 1 through a(7) = 11 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(31) (41) (42) (52)
(211) (221) (51) (61)
(311) (321) (322)
(2111) (411) (331)
(2211) (421)
(3111) (511)
(2221)
(3211)
(4111)
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>=0, 1, 0),
`if`(i<1, 0, add(b(n-i*j, i-1, t+`if`(j>0, 2, 0)-j), j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50); # Alois P. Heinz, Mar 19 2023
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], 2*Length[Union[#]]>=Length[#]&]], {n, 0, 30}]
CROSSREFS
The complement is counted by A360254, ranks A360558.
These partitions have ranks A361395.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by length, reverse A058398.
A067538 counts partitions with integer mean, strict A102627.
A116608 counts partitions by number of distinct parts.
Sequence in context: A286736 A241383 A258125 * A147982 A329899 A051466
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2023
STATUS
approved