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A351005
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Number of integer partitions of n into parts that are alternately equal and unequal.
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33
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1, 1, 2, 1, 2, 2, 3, 2, 4, 2, 5, 4, 6, 4, 8, 5, 10, 6, 12, 8, 16, 9, 18, 12, 22, 14, 28, 16, 33, 20, 40, 24, 48, 28, 56, 34, 67, 40, 80, 46, 94, 56, 110, 64, 130, 75, 152, 88, 176, 102, 206, 118, 238, 138, 276, 159, 320, 182, 368, 210, 424, 242, 488, 276, 558
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OFFSET
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0,3
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COMMENTS
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Also partitions whose multiplicities are all 2's, except possibly for the last, which may be 1.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(12) = 6 partitions (A..C = 10..12):
1 2 3 4 5 6 7 8 9 A B C
11 22 221 33 331 44 441 55 443 66
2211 332 442 551 552
3311 3322 33221 4422
4411 5511
332211
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And@@Table[#[[i]]==#[[i+1]], {i, 1, Length[#]-1, 2}]&&And@@Table[#[[i]]!=#[[i+1]], {i, 2, Length[#]-1, 2}]&]], {n, 0, 30}]
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CROSSREFS
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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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