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 A367395 Number of strict integer partitions of n whose length is the sum of two distinct parts. 8
 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 7, 8, 11, 13, 17, 19, 25, 28, 35, 41, 49, 57, 68, 78, 92, 107, 124, 143, 166, 192, 220, 254, 291, 335, 382, 439, 499, 572, 649, 741, 840, 956, 1080, 1226, 1383, 1566, 1762, 1988, 2235, 2515, 2822, 3166, 3547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Table of n, a(n) for n=0..59. EXAMPLE The strict partition (5,3,2,1) has 4 = 3 + 1 so is counted under a(11). The a(6) = 1 through a(17) = 7 strict partitions (A..E = 10..14): 321 421 521 621 721 821 921 A21 B21 C21 D21 E21 4321 5321 6321 5431 6431 6531 7531 7631 7321 8321 7431 8431 8531 9321 A321 9431 54321 64321 B321 65321 74321 MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&MemberQ[Total/@Subsets[#, {2}], Length[#]]&]], {n, 0, 30}] CROSSREFS The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum, linear combination, or semi-sum of the parts. The current sequence is starred. sum-full sum-free comb-full comb-free semi-full semi-free ----------------------------------------------------------- partitions: A367212 A367213 A367218 A367219 A367394 A367398 strict: A367214 A367215 A367220 A367221 A367395* A367399 subsets: A367216 A367217 A367222 A367223 A367396 A367400 ranks: A367224 A367225 A367226 A367227 A367397 A367401 A000041 counts partitions, strict A000009. A002865 counts partitions whose length is a part, complement A229816. A088809/A093971 count twofold sum-full subsets. A236912 counts partitions containing no semi-sum, ranks A364461. A237113 counts partitions containing a semi-sum, ranks A364462. A237668 counts sum-full partitions, sum-free A237667. A366738 counts semi-sums of partitions, strict A366741. Triangles: A008284 counts partitions by length, strict A008289. A365541 counts subsets with a semi-sum k. A367404 counts partitions with a semi-sum k, strict A367405. Cf. A000700, A238628, A363225, A364272, A364534, A365661, A365925, A367410, A367411. Sequence in context: A210955 A051697 A240869 * A065308 A035680 A238220 Adjacent sequences: A367392 A367393 A367394 * A367396 A367397 A367398 KEYWORD nonn AUTHOR Gus Wiseman, Nov 19 2023 STATUS approved

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Last modified September 18 01:35 EDT 2024. Contains 375995 sequences. (Running on oeis4.)