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A325716
Number of separable partitions of n in which the number of distinct (repeatable) parts is > 1.
0
0, 0, 1, 2, 4, 5, 9, 13, 18, 25, 36, 48, 65, 86, 115, 151, 197, 253, 328, 421, 535, 677, 857, 1076, 1348, 1680, 2088, 2586, 3192, 3926, 4819, 5896, 7190, 8748, 10622, 12860, 15534, 18723, 22517, 27028, 32372, 38696, 46173, 54997, 65381, 77600, 91949, 108776
OFFSET
1,4
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) = -1 + A325534(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]]>1&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A060312 A218934 A348176 * A068372 A068370 A364467
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 17 2019
STATUS
approved