login
A325720
Number of separable partitions of n in which the number of distinct (repeatable) parts is > 5.
0
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, 254, 388, 568, 830, 1169, 1645, 2270, 3096, 4161, 5556, 7312, 9572, 12402, 15962, 20386, 25851, 32595, 40850, 50938, 63148, 77979, 95773, 117231, 142777, 173387
OFFSET
1,22
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) - A325714(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]]>5&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A328548 A294536 A325650 * A103924 A160647 A103925
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 19 2019
STATUS
approved