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A362051
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Number of integer partitions of 2n without a nonempty initial consecutive subsequence summing to n.
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4
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1, 1, 2, 6, 11, 27, 44, 93, 149, 271, 432, 744, 1109, 1849, 2764, 4287, 6328, 9673, 13853, 20717, 29343, 42609, 60100, 85893, 118475, 167453, 230080, 318654, 433763, 595921, 800878, 1090189, 1456095, 1957032, 2600199, 3465459, 4558785, 6041381, 7908681
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OFFSET
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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The a(1) = 1 through a(4) = 11 partitions:
(2) (4) (6) (8)
(31) (42) (53)
(51) (62)
(222) (71)
(411) (332)
(2211) (521)
(611)
(3221)
(3311)
(5111)
(32111)
The partition y = (3,2,1,1,1) has nonempty initial consecutive subsequences (3,2,1,1,1), (3,2,1,1), (3,2,1), (3,2), (3), with sums 8, 7, 6, 5, 3. Since 4 is missing, y is counted under a(4).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[2n], !MemberQ[Accumulate[#], n]&]], {n, 0, 15}]
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CROSSREFS
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The complement is counted by A322439.
A304442 counts partitions with all equal run-sums.
A353836 counts partitions by number of distinct run-sums.
Cf. A108917, A169942, A237363, A325676, A353864, A360254, A360672, A360675, A360686, A360952, A362560.
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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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