A338332 Number of relatively prime 3-part integer partitions of n with no 1's.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 3, 8, 6, 9, 9, 16, 10, 21, 15, 22, 20, 33, 21, 38, 30, 41, 35, 56, 34, 65, 49, 64, 56, 79, 55, 96, 72, 93, 77, 120, 76, 133, 99, 122, 110, 161, 105, 172, 126, 167, 143, 208, 136, 213, 165, 212, 182, 261, 163, 280, 210, 257

Offset

0,10

Comments

The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (length 3), and A289509 (relatively prime).

Links

Table of n, a(n) for n=0..63.

Example

The a(7) = 1 through a(17) = 16 triples (A = 10, B = 11, C = 12, D = 13):
  322   332   432   433   443   543   544   554   654   655   665
              522   532   533   552   553   653   744   754   755
                          542   732   643   743   753   763   764
                          632         652   752   762   772   773
                          722         733   833   843   853   854
                                      742   932   852   943   863
                                      832         942   952   872
                                      922         A32   A33   944
                                                  B22   B32   953
                                                              962
                                                              A43
                                                              A52
                                                              B33
                                                              B42
                                                              C32
                                                              D22

Mathematica

Table[Length[Select[IntegerPartitions[n, {3}], !MemberQ[#, 1]&&GCD@@#==1&]], {n, 0, 30}]

Crossrefs

A001399(n-6) does not require relative primality.

A005408 /\ A014612 /\ A289509 gives the Heinz numbers of these partitions.

A055684 is the 2-part version.

A284825 counts the case that is also pairwise non-coprime.

A302698 counts these partitions of any length.

A337563 is the pairwise coprime instead of relatively prime version.

A338333 is the strict version.

A000837 counts relatively prime partitions, with strict case A078374.

A008284 counts partitions by sum and length.

Cf. A000010, A000741, A023022, A078374, A082024, A101271, A307719, A337450, A337599, A337600, A337601.

Sequence in context: A266981 A045893 A071939 * A075545 A006307 A152991

Adjacent sequences: A338329 A338330 A338331 * A338333 A338334 A338335

Keyword

nonn

Author

Gus Wiseman, Oct 30 2020

Status

approved