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 A325648 #6 May 16 2019 17:33:48 %S A325648 0,0,0,0,0,0,0,0,0,1,2,5,10,19,28,48,69,102,138,190,254,331,420,534, %T A325648 662,818,1003,1192,1438,1700,2011,2334,2746,3127,3625,4132,4728,5311, %U A325648 6066,6737,7624,8446,9476,10437,11648,12731,14133,15421,16991,18461,20286 %N A325648 Number of separable partitions of n in which the number of distinct (repeatable) parts is 4. %C A325648 A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325646 for a guide to related sequences. %e A325648 a(11) counts these 2 partitions: [4,1,3,2,1], [3,2,1,2,1,2]. %t A325648 (separable=Table[Map[#[[1]]&,Select[Map[{#,Quotient[(1+Length[#]),Max[Map[Length,Split[#]]]]}&,IntegerPartitions[nn]],#[[2]]>1&]],{nn,35}]); %t A325648 Map[Length[Select[Map[{#,Length[Union[#]]}&,#],#[[2]]==4&]]&,separable] %t A325648 (* _Peter J. C. Moses_, May 08 2019 *) %Y A325648 Cf. A000041, A325646. %K A325648 nonn,easy %O A325648 1,11 %A A325648 _Clark Kimberling_, May 16 2019