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A346634
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Number of strict odd-length integer partitions of 2n + 1.
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2
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1, 1, 1, 2, 4, 6, 9, 14, 19, 27, 38, 52, 71, 96, 128, 170, 224, 293, 380, 491, 630, 805, 1024, 1295, 1632, 2048, 2560, 3189, 3958, 4896, 6038, 7424, 9100, 11125, 13565, 16496, 20013, 24223, 29250, 35244, 42378, 50849, 60896, 72789, 86841, 103424, 122960, 145937
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(0) = 1 through a(7) = 14 partitions:
(1) (3) (5) (7) (9) (11) (13) (15)
(4,2,1) (4,3,2) (5,4,2) (6,4,3) (6,5,4)
(5,3,1) (6,3,2) (6,5,2) (7,5,3)
(6,2,1) (6,4,1) (7,4,2) (7,6,2)
(7,3,1) (7,5,1) (8,4,3)
(8,2,1) (8,3,2) (8,5,2)
(8,4,1) (8,6,1)
(9,3,1) (9,4,2)
(10,2,1) (9,5,1)
(10,3,2)
(10,4,1)
(11,3,1)
(12,2,1)
(5,4,3,2,1)
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2, 0,
`if`(n=0, t, add(b(n-i*j, i-1, abs(t-j)), j=0..min(n/i, 1))))
end:
a:= n-> b(2*n+1$2, 0):
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[2n+1], UnsameQ@@#&&OddQ[Length[#]]&]], {n, 0, 15}]
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CROSSREFS
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The even version is the even bisection of A067661.
The case of all odd parts is counted by A069911 (non-strict: A078408).
A340385 counts partitions with odd length and maximum, ranked by A340386.
Other cases of odd length:
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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