cp's OEIS Frontend

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

%I A338332 #5 Nov 05 2020 22:56:08
%S A338332 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,
%T A338332 35,56,34,65,49,64,56,79,55,96,72,93,77,120,76,133,99,122,110,161,105,
%U A338332 172,126,167,143,208,136,213,165,212,182,261,163,280,210,257
%N A338332 Number of relatively prime 3-part integer partitions of n with no 1's.
%C A338332 The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (length 3), and A289509 (relatively prime).
%e A338332 The a(7) = 1 through a(17) = 16 triples (A = 10, B = 11, C = 12, D = 13):
%e A338332   322   332   432   433   443   543   544   554   654   655   665
%e A338332               522   532   533   552   553   653   744   754   755
%e A338332                           542   732   643   743   753   763   764
%e A338332                           632         652   752   762   772   773
%e A338332                           722         733   833   843   853   854
%e A338332                                       742   932   852   943   863
%e A338332                                       832         942   952   872
%e A338332                                       922         A32   A33   944
%e A338332                                                   B22   B32   953
%e A338332                                                               962
%e A338332                                                               A43
%e A338332                                                               A52
%e A338332                                                               B33
%e A338332                                                               B42
%e A338332                                                               C32
%e A338332                                                               D22
%t A338332 Table[Length[Select[IntegerPartitions[n,{3}],!MemberQ[#,1]&&GCD@@#==1&]],{n,0,30}]
%Y A338332 A001399(n-6) does not require relative primality.
%Y A338332 A005408 /\ A014612 /\ A289509 gives the Heinz numbers of these partitions.
%Y A338332 A055684 is the 2-part version.
%Y A338332 A284825 counts the case that is also pairwise non-coprime.
%Y A338332 A302698 counts these partitions of any length.
%Y A338332 A337563 is the pairwise coprime instead of relatively prime version.
%Y A338332 A338333 is the strict version.
%Y A338332 A000837 counts relatively prime partitions, with strict case A078374.
%Y A338332 A008284 counts partitions by sum and length.
%Y A338332 Cf. A000010, A000741, A023022, A078374, A082024, A101271, A307719, A337450, A337599, A337600, A337601.
%K A338332 nonn
%O A338332 0,10
%A A338332 _Gus Wiseman_, Oct 30 2020