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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Even bisection of A362558. a(0) = 1; a(n) = A000041(2n) - A322439(n). - Alois P. Heinz, Apr 27 2023 LINKS Table of n, a(n) for n=0..38. 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 version for compositions is A000302, bisection of A213173. The complement is counted by A322439. Even bisection of A362558. A000041 counts integer partitions, strict A000009. A304442 counts partitions with all equal run-sums. A325347 counts partitions with integer median, complement A307683. A353836 counts partitions by number of distinct run-sums. A359893/A359901/A359902 count partitions by median. Cf. A108917, A169942, A237363, A325676, A353864, A360254, A360672, A360675, A360686, A360952, A362560. Sequence in context: A007186 A033304 A091622 * A191315 A184884 A275222 Adjacent sequences: A362048 A362049 A362050 * A362052 A362053 A362054 KEYWORD nonn AUTHOR Gus Wiseman, Apr 24 2023 STATUS approved

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Last modified November 30 03:08 EST 2023. Contains 367452 sequences. (Running on oeis4.)