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%I #6 May 16 2019 17:33:56
%S 0,0,0,0,0,1,2,5,9,13,21,29,39,49,68,79,101,116,145,167,196,221,262,
%T 287,335,368,412,460,512,554,617,673,723,800,865,925,1001,1090,1140,
%U 1250,1317,1418,1493,1619,1665,1828,1884,2022,2098,2275,2308,2520,2564
%N Number of separable partitions of n in which the number of distinct (repeatable) parts is 3.
%C A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325646 for a guide to related sequences.
%e a(8) counts these 5 partitions: [5,2,1], [4,3,1], [1,4,1,2], [2,3,2,1], [1,3,1,2,1].
%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]]==3&]]&,separable]
%t (* _Peter J. C. Moses_, May 08 2019 *)
%Y Cf. A000041, A325334, A325646.
%K nonn,easy
%O 1,7
%A _Clark Kimberling_, May 16 2019
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