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A351595
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Number of odd-length integer partitions y of n such that y_i > y_{i+1} for all even i.
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5
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0, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 9, 10, 13, 16, 20, 24, 30, 35, 44, 52, 63, 74, 90, 105, 126, 148, 175, 204, 242, 280, 330, 382, 446, 515, 600, 690, 800, 919, 1060, 1214, 1398, 1595, 1830, 2086, 2384, 2711, 3092, 3506, 3988, 4516, 5122, 5788, 6552, 7388, 8345
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OFFSET
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0,6
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LINKS
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EXAMPLE
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The a(1) = 1 through a(12) = 10 partitions (A..C = 10..12):
1 2 3 4 5 6 7 8 9 A B C
221 321 331 332 432 442 443 543
421 431 441 532 542 552
521 531 541 551 642
621 631 632 651
721 641 732
731 741
821 831
33221 921
43221
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&And@@Table[#[[i]]>#[[i+1]], {i, 2, Length[#]-1, 2}]&]], {n, 0, 30}]
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CROSSREFS
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The ordered version (compositions) is A000213 shifted right once.
All odd-length partitions are counted by A027193.
This appears to be the odd-length case of A122135, even-length A122134.
The case that is constant at odd indices:
For equality instead of inequality:
- odd-length: A000009 (except at 0)
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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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