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 A308410 a(n) is the number of partitions p = p(1) >= p(2) >= ... >= p(k) of n whose alternating sum is a part of p. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE 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. MATHEMATICA Map[Count[Map[Apply[MemberQ, {#, Total[Map[ Total, {Take[##], Drop[##]} &[#, {1, -1, 2}] {1, -1}]]}] &, IntegerPartitions[#]], True] &, Range[40]] (* Peter J. C. Moses, May 25 2019 *) CROSSREFS Cf. A000041, A308230. Sequence in context: A194012 A255556 A331462 * A286111 A240574 A050061 Adjacent sequences:  A308407 A308408 A308409 * A308411 A308412 A308413 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 05 2019 STATUS approved

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Last modified October 20 21:32 EDT 2020. Contains 337910 sequences. (Running on oeis4.)