A325720 - OEIS

%I #4 May 20 2019 05:35:06

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10,20,36,64,101,166,

%T 254,388,568,830,1169,1645,2270,3096,4161,5556,7312,9572,12402,15962,

%U 20386,25851,32595,40850,50938,63148,77979,95773,117231,142777,173387

%N Number of separable partitions of n in which the number of distinct (repeatable) parts is > 5.

%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.

%F a(n) = A325534(n) - A325714(n) for n >= 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]]>5&]]&,separable]

%t (* _Peter J. C. Moses_, May 08 2019 *)

%Y Cf. A000041, A325534.

%K nonn,easy

%O 1,22

%A _Clark Kimberling_, May 19 2019