This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325534 #21 Aug 04 2025 19:44:44
%S A325534 1,1,1,2,3,5,6,10,14,19,26,37,49,66,87,116,152,198,254,329,422,536,
%T A325534 678,858,1077,1349,1681,2089,2587,3193,3927,4820,5897,7191,8749,10623,
%U A325534 12861,15535,18724,22518,27029,32373,38697,46174,54998,65382,77601,91950,108777
%N A325534 Number of separable partitions of n; see Comments.
%C A325534 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 A325534 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 A325534 Andrew Howroyd, <a href="/A325534/b325534.txt">Table of n, a(n) for n = 0..1000</a>
%F A325534 a(n) = A000041(n) - A325535(n).
%e A325534 For n=5, the partition 1+2+2 is separable as 2+1+2, and 2+1+1+1 is inseparable.
%t A325534 Table[Length[Select[Map[Quotient[(1 + Length[#]), Max[Map[Length, Split[#]]]] &,
%t A325534 IntegerPartitions[nn]], # > 1 &]], {nn, 50}] (* _Peter J. C. Moses_, May 07 2019 *)
%Y A325534 Cf. A000041, A238589, A325535.
%K A325534 nonn,easy
%O A325534 0,4
%A A325534 _Clark Kimberling_, May 08 2019
%E A325534 a(0)=1 prepended by _Alois P. Heinz_, Jan 20 2024