%I #19 Jan 31 2024 22:23:30
%S 1,1,1,2,3,5,6,10,14,19,26,37,49,66,87,116,152,198,254,329,422,536,
%T 678,858,1077,1349,1681,2089,2587,3193,3927,4820,5897,7191,8749,10623,
%U 12861,15535,18724,22518,27029,32373,38697,46174,54998,65382,77601,91950,108777
%N Number of separable partitions of n; see Comments.
%C Definition: a partition is separable if there is an ordering of its parts in which no consecutive parts are identical; otherwise the partition is inseparable.
%C A partition with k parts is separable if and only if there is no part whose multiplicity is greater than ceiling(k/2). - _Andrew Howroyd_, Jan 31 2024
%H Andrew Howroyd, <a href="/A325534/b325534.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) + A325535(n) = A000041(n) = number of partitions of n.
%e For n=5, the partition 1+2+2 is separable as 2+1+2, and 2+1+1+1 is inseparable.
%t Table[Length[Select[Map[Quotient[(1 + Length[#]), Max[Map[Length, Split[#]]]] &,
%t IntegerPartitions[nn]], # > 1 &]], {nn, 50}] (* _Peter J. C. Moses_, May 07 2019 *)
%Y Cf. A000041, A238589, A325535.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, May 08 2019
%E a(0)=1 prepended by _Alois P. Heinz_, Jan 20 2024