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A325717
Number of separable partitions of n in which the number of distinct (repeatable) parts is > 2.
0
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
1,7
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.
FORMULA
a(n) = A325534(n) - A325711(n) for n >= 1.
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 *)
CROSSREFS
Sequence in context: A199935 A090937 A338666 * A291942 A071609 A377061
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 17 2019
STATUS
approved