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 A338333 Number of relatively prime 3-part strict integer partitions of n with no 1's. 4
 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 7, 6, 10, 8, 14, 12, 18, 16, 24, 18, 30, 25, 34, 30, 44, 31, 52, 42, 56, 49, 69, 50, 80, 64, 83, 70, 102, 71, 114, 90, 112, 100, 140, 98, 153, 117, 153, 132, 184, 128, 195, 154, 196, 169, 234, 156, 252, 196, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS The Heinz numbers of these partitions are the intersection of A005117 (strict), A005408 (no 1's), A014612 (length 3), and A289509 (relatively prime). LINKS EXAMPLE The a(9) = 1 through a(19) = 14 triples (A = 10, B = 11, C = 12, D = 13, E = 14):   432   532   542   543   643   653   654   754   764   765   865               632   732   652   743   753   763   854   873   874                           742   752   762   853   863   954   964                           832   932   843   943   872   972   973                                       852   952   953   A53   982                                       942   B32   962   B43   A54                                       A32         A43   B52   A63                                                   A52   D32   A72                                                   B42         B53                                                   C32         B62                                                               C43                                                               C52                                                               D42                                                               E32 MATHEMATICA Table[Length[Select[IntegerPartitions[n, {3}], UnsameQ@@#&&!MemberQ[#, 1]&&GCD@@#==1&]], {n, 0, 30}] CROSSREFS A001399(n-9) does not require relative primality. A005117 /\ A005408 /\ A014612 /\ A289509 gives the Heinz numbers. A055684 is the 2-part version. A284825 counts the case that is also pairwise non-coprime. A337452 counts these partitions of any length. A337563 is the pairwise coprime instead of relatively prime version. A337605 is the pairwise non-coprime instead of relative prime version. A338332 is the not necessarily strict version. A338333*6 is the ordered version. A000837 counts relatively prime partitions. A008284 counts partitions by sum and length. A078374 counts relatively prime strict partitions. A101271 counts 3-part relatively prime strict partitions. A220377 counts 3-part pairwise coprime strict partitions. A337601 counts 3-part partitions whose distinct parts are pairwise coprime. Cf. A000010, A000217, A000741, A023022, A082024, A302698, A307719, A337450, A337599, A338468. Sequence in context: A267261 A219027 A341949 * A287144 A085893 A341950 Adjacent sequences:  A338330 A338331 A338332 * A338334 A338335 A338336 KEYWORD nonn AUTHOR Gus Wiseman, Oct 30 2020 STATUS approved

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Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)