A325717 Number of separable partitions of n in which the number of distinct (repeatable) parts is > 2.

0, 0, 0, 0, 0, 1, 2, 5, 9, 14, 23, 34, 49, 68, 97, 129, 175, 228, 303, 392, 507, 645, 826, 1038, 1314, 1641, 2050, 2542, 3152, 3877, 4776, 5844, 7142, 8695, 10572, 12797, 15482, 18663, 22459, 26959, 32314, 38623, 46112, 54923, 65311, 77526, 91882, 108686

Offset: 1

Author

Clark Kimberling, May 17 2019

Keywords

• nonn
• easy

Comments

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.

Crossrefs

Cf. A000041, A325534.

Programs

Mathematica

(separable=Table[Map[#[[1]]&,Select[Map[{#,Quotient[(1+Length[#]),Max[Map[Length,Split[#]]]]}&,IntegerPartitions[nn]],#[[2]]>1&]],{nn,35}]);
Map[Length[Select[Map[{#,Length[Union[#]]}&,#],#[[2]]>2&]]&,separable]
(* Peter J. C. Moses, May 08 2019 *)

Formula

a(n) = A325534(n) - A325711(n) for n >= 1.