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A363532
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Number of integer partitions of n with weighted alternating sum 0.
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9
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1, 0, 0, 1, 0, 0, 2, 2, 0, 3, 3, 3, 5, 5, 10, 12, 7, 14, 25, 18, 22, 48, 48, 41, 67, 82, 89, 111, 140, 170, 220, 214, 264, 392, 386, 436, 623, 693, 756, 934, 1102, 1301, 1565, 1697, 2132, 2616, 2727, 3192, 4062, 4550, 5000, 6132, 7197, 8067, 9338, 10750, 12683
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OFFSET
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0,7
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COMMENTS
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We define the weighted alternating sum of a sequence (y_1,...,y_k) to be Sum_{i=1..k} (-1)^(i-1) * i * y_i.
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LINKS
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EXAMPLE
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The a(11) = 3 through a(15) = 12 partitions (A = 10):
(33221) (84) (751) (662) (A5)
(44111) (6222) (5332) (4442) (8322)
(222221) (7311) (6421) (5531) (9411)
(621111) (532111) (43331) (722211)
(51111111) (42211111) (54221) (831111)
(65111) (3322221)
(432221) (3333111)
(443111) (4422111)
(32222111) (5511111)
(33311111) (22222221)
(72111111)
(6111111111)
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MATHEMATICA
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altwtsum[y_]:=Sum[(-1)^(k-1)*k*y[[k]], {k, 1, Length[y]}];
Table[Length[Select[IntegerPartitions[n], altwtsum[#]==0&]], {n, 0, 30}]
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CROSSREFS
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These partitions have ranks A363621.
The version for compositions is A363626.
A363619 gives weighted alternating sum of prime indices, reverse A363620.
A363624 gives weighted alternating sum of Heinz partition, reverse A363625.
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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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