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A308410
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a(n) is the number of partitions p = p(1) >= p(2) >= ... >= p(k) of n whose alternating sum is a part of p.
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0
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1, 1, 3, 2, 5, 6, 10, 10, 20, 18, 33, 35, 55, 59, 92, 97, 146, 161, 231, 251, 363, 393, 551, 609, 828, 924, 1240, 1382, 1824, 2055, 2665, 3004, 3870, 4359, 5551, 6280, 7910, 8957, 11201, 12683, 15728, 17857, 21951, 24939, 30472, 34625, 42031, 47803, 57677
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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(6) = 6 partitions of 6 to be counted are these:
[6] has alternating sum 6, which is a part,
[4,2] has alternating sum 4 - 2 = 2, a part,
[4,1,1] has alternating sum 4 - 1 + 1 = 4,
[3,2,1] has alternating sum 3 - 2 + 1 = 2,
[2,2,2] has alternating sum 2 - 2 + 1 = 2, and
[2,1,1,1,1] has alternating sum 2 - 1 + 1 - 1 + 1 - 1 = 2.
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MATHEMATICA
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Map[Count[Map[Apply[MemberQ, {#, Total[Map[
Total, {Take[##], Drop[##]} &[#, {1, -1, 2}] {1, -1}]]}] &,
IntegerPartitions[#]], True] &, Range[40]]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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