

A362051


Number of integer partitions of 2n without a nonempty initial consecutive subsequence summing to n.


4



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

0,3


COMMENTS



LINKS



EXAMPLE

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).


MATHEMATICA

Table[Length[Select[IntegerPartitions[2n], !MemberQ[Accumulate[#], n]&]], {n, 0, 15}]


CROSSREFS

The complement is counted by A322439.
A304442 counts partitions with all equal runsums.
A353836 counts partitions by number of distinct runsums.
Cf. A108917, A169942, A237363, A325676, A353864, A360254, A360672, A360675, A360686, A360952, A362560.


KEYWORD

nonn


AUTHOR



STATUS

approved



