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 A301854 Number of positive special sums of integer partitions of n. 13
 1, 3, 7, 13, 25, 40, 67, 100, 158, 220, 336, 452, 649, 862, 1228, 1553, 2155, 2738, 3674, 4612, 6124, 7497, 9857, 12118, 15524, 18821, 24152, 28863, 36549, 44002, 54576, 65125, 80943, 95470, 117991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A positive special sum of an integer partition y is a number n > 0 such that exactly one submultiset of y sums to n. LINKS EXAMPLE The a(4) = 13 special positive subset-sums: 1<=(1111), 2<=(1111), 3<=(1111), 4<=(1111), 1<=(211),  3<=(211),  4<=(211), 1<=(31),   3<=(31),   4<=(31), 2<=(22),   4<=(22), 4<=(4). MATHEMATICA uqsubs[y_]:=Join@@Select[GatherBy[Union[Rest[Subsets[y]]], Total], Length[#]===1&]; Table[Total[Length/@uqsubs/@IntegerPartitions[n]], {n, 25}] CROSSREFS Cf. A000712, A108917, A122768, A275972, A276024, A284640, A299701, A299702, A299729, A301829, A301830, A301854, A301855, A301856. Sequence in context: A056764 A026103 A328652 * A092463 A259343 A210613 Adjacent sequences:  A301851 A301852 A301853 * A301855 A301856 A301857 KEYWORD nonn,more AUTHOR Gus Wiseman, Mar 27 2018 EXTENSIONS a(21)-a(35) from Alois P. Heinz, Apr 08 2018 STATUS approved

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Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)