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A340385
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Number of integer partitions of n into an odd number of parts, the greatest of which is odd.
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18
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1, 0, 2, 0, 3, 1, 6, 3, 10, 7, 18, 15, 30, 28, 51, 50, 82, 87, 134, 145, 211, 235, 331, 375, 510, 586, 779, 901, 1172, 1366, 1750, 2045, 2581, 3026, 3778, 4433, 5476, 6430, 7878, 9246, 11240, 13189, 15931, 18670, 22417, 26242, 31349, 36646, 43567, 50854
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OFFSET
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1,3
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LINKS
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EXAMPLE
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The a(3) = 2 through a(10) = 7 partitions:
3 5 321 7 332 9 532
111 311 322 521 333 541
11111 331 32111 522 721
511 531 32221
31111 711 33211
1111111 32211 52111
33111 3211111
51111
3111111
111111111
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]*Max[#]]&]], {n, 30}]
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CROSSREFS
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Partitions with odd maximum are counted by A027193, ranked by A244991.
The Heinz numbers of these partitions are given by A340386.
Other cases of odd length:
- A024429 counts set partitions of odd length.
- A067659 counts strict partitions of odd length.
- A089677 counts ordered set partitions of odd length.
- A166444 counts compositions of odd length.
- A174726 counts ordered factorizations of odd length.
- A332304 counts strict compositions of odd length.
- A339890 counts factorizations of odd length.
A026804 counts partitions whose least part is odd.
A072233 counts partitions by sum and length.
A101707 counts partitions with odd rank.
A160786 counts odd-length partitions of odd numbers, ranked by A300272.
A340101 counts factorizations into odd factors.
A340102 counts odd-length factorizations into odd factors.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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