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A343942 Number of even-length strict integer partitions of 2n+1. 5
0, 1, 2, 3, 4, 6, 9, 13, 19, 27, 38, 52, 71, 96, 128, 170, 224, 292, 380, 491, 630, 805, 1024, 1295, 1632, 2049, 2560, 3189, 3959, 4896, 6038, 7424, 9100, 11125, 13565, 16496, 20013, 24223, 29249, 35244, 42378, 50849, 60896, 72789, 86841, 103424, 122960, 145937, 172928 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
By conjugation, also the number of integer partitions of 2n+1 covering an initial interval of positive integers with greatest part even.
LINKS
FORMULA
The Heinz numbers are A005117 /\ A028260 /\ A300063.
EXAMPLE
The a(1) = 1 through a(7) = 13 strict partitions:
(2,1) (3,2) (4,3) (5,4) (6,5) (7,6) (8,7)
(4,1) (5,2) (6,3) (7,4) (8,5) (9,6)
(6,1) (7,2) (8,3) (9,4) (10,5)
(8,1) (9,2) (10,3) (11,4)
(10,1) (11,2) (12,3)
(5,3,2,1) (12,1) (13,2)
(5,4,3,1) (14,1)
(6,4,2,1) (6,4,3,2)
(7,3,2,1) (6,5,3,1)
(7,4,3,1)
(7,5,2,1)
(8,4,2,1)
(9,3,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[2n+1], UnsameQ@@#&&EvenQ[Length[#]]&]], {n, 0, 15}]
CROSSREFS
Ranked by A005117 (strict), A028260 (even length), and A300063 (odd sum).
Odd bisection of A067661 (non-strict: A027187).
The non-strict version is A236914.
The opposite type of strict partition (odd length and even sum) is A344650.
A000041 counts partitions of 2n with alternating sum 0, ranked by A000290.
A103919 counts partitions by sum and alternating sum (reverse: A344612).
A344610 counts partitions by sum and positive reverse-alternating sum.
Sequence in context: A098889 A061481 A017824 * A094054 A001521 A003143
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 09 2021
EXTENSIONS
More terms from Bert Dobbelaere, Jun 12 2021
STATUS
approved

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Last modified June 17 06:25 EDT 2024. Contains 373432 sequences. (Running on oeis4.)