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A364055
Number of integer partitions of n satisfying (length) = (mean). Partitions of n into sqrt(n) parts.
1
1, 1, 0, 0, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8033, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55974, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,5
FORMULA
a(n^2) = A206240(n).
EXAMPLE
The a(0) = 1 through a(9) = 7 partitions:
() (1) . . (22) . . . . (333)
(31) (432)
(441)
(522)
(531)
(621)
(711)
MATHEMATICA
Table[Length[If[n==0, {{}}, Select[IntegerPartitions[n], Mean[#]==Length[#]&]]], {n, 0, 30}]
CROSSREFS
The strict case is A107379(sqrt(n)).
Without zeros we have A206240.
These partitions have ranks A363951.
A008284 counts partitions by length, A058398 by mean.
A067538 counts partitions with integer mean, ranks A316413.
Sequence in context: A318329 A107503 A350731 * A184366 A230614 A230730
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 07 2023
STATUS
approved