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Number of separable partitions of n in which the number of distinct (repeatable) parts is > 2.
0

%I #4 May 19 2019 20:34:42

%S 0,0,0,0,0,1,2,5,9,14,23,34,49,68,97,129,175,228,303,392,507,645,826,

%T 1038,1314,1641,2050,2542,3152,3877,4776,5844,7142,8695,10572,12797,

%U 15482,18663,22459,26959,32314,38623,46112,54923,65311,77526,91882,108686

%N Number of separable partitions of n in which the number of distinct (repeatable) parts is > 2.

%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) - A325711(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]]>2&]]&,separable]

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

%Y Cf. A000041, A325534.

%K nonn,easy

%O 1,7

%A _Clark Kimberling_, May 17 2019