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A351593
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Number of odd-length integer partitions of n into parts that are alternately equal and strictly decreasing.
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4
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0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 3, 5, 4, 6, 4, 8, 6, 9, 6, 12, 7, 14, 10, 16, 11, 20, 13, 24, 16, 28, 18, 34, 21, 40, 26, 46, 30, 56, 34, 64, 41, 75, 48, 88, 54, 102, 64, 118, 73, 138, 84, 159, 98, 182, 112, 210, 128, 242, 148, 276, 168, 318
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OFFSET
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0,6
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COMMENTS
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Also odd-length partitions whose run-lengths are all 2's, except for the last, which is 1.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(15) = 6 partitions (A..F = 10..15):
1 2 3 4 5 6 7 8 9 A B C D E F
221 331 332 441 442 443 552 553 554 663
551 661 662 771
33221 44221 44331
55221
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&And@@Table[If[EvenQ[i], #[[i]]!=#[[i+1]], #[[i]]==#[[i+1]]], {i, Length[#]-1}]&]], {n, 0, 30}]
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CROSSREFS
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With only equalities we get:
- opposite odd-length: A000009 (except at 0)
Without equalities we get:
- opposite any length: A122129 (apparently)
- opposite odd-length: A122130 (apparently)
- even-length: A122134 (apparently)
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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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