The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 May 16 2019 21:18:43
%S 1,1,2,3,5,6,10,14,19,26,37,49,66,87,115,150,193,244,309,387,479,585,
%T 714,860,1032,1226,1454,1697,1991,2304,2672,3060,3518,3981,4541,5121,
%U 5782,6462,7265,8057,9000,9938,11031,12131,13384,14634,16085,17534,19161
%N Number of separable partitions of n in which the number of distinct (repeatable) parts <= 4.
%C A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325534 for a guide to related sequences.
%t (separable=Table[Map[#[[1]]&,Select[Map[{#,Quotient[(1+Length[#]),Max[Map[Length,Split[#]]]]}&,IntegerPartitions[nn]],#[[2]]>1&]],{nn,35}]);
%t Map[Length[Select[Map[{#,Length[Union[#]]}&,#],#[[2]]<=4&]]&,separable]
%t (* _Peter J. C. Moses_, May 08 2019 *)
%Y Cf. A000041, A325334.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, May 16 2019