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 A325245 #7 Apr 16 2019 15:26:56
%S A325245 0,0,0,1,1,2,4,4,6,8,11,11,19,17,25,29,37,37,56,53,75,80,99,103,145,
%T A325245 143,181,199,247,255,336,339,426,459,548,590,738,759,916,999,1192,
%U A325245 1259,1529,1609,1915,2083,2406,2589,3085,3267,3809,4134,4763,5119,5964
%N A325245 Number of integer partitions of n with adjusted frequency depth 3.
%C A325245 The adjusted frequency depth of an integer partition is 0 if the partition is empty, and otherwise it is 1 plus the number of times one must take the multiset of multiplicities to reach a singleton. For example, the partition (32211) has adjusted frequency depth 5 because we have: (32211) -> (221) -> (21) -> (11) -> (2). The enumeration of integer partitions by adjusted frequency depth is given by A325280. The adjusted frequency depth of the integer partition with Heinz number n is given by A323014.
%e A325245 The a(3) = 1 through a(10) = 11 partitions:
%e A325245 (21) (31) (32) (42) (43) (53) (54) (64)
%e A325245 (41) (51) (52) (62) (63) (73)
%e A325245 (321) (61) (71) (72) (82)
%e A325245 (2211) (421) (431) (81) (91)
%e A325245 (521) (432) (532)
%e A325245 (3311) (531) (541)
%e A325245 (621) (631)
%e A325245 (222111) (721)
%e A325245 (3322)
%e A325245 (4321)
%e A325245 (4411)
%t A325245 fdadj[ptn_List]:=If[ptn=={},0,Length[NestWhileList[Sort[Length/@Split[#]]&,ptn,Length[#]>1&]]];
%t A325245 Table[Length[Select[IntegerPartitions[n],fdadj[#]==3&]],{n,0,30}]
%Y A325245 Column k = 3 of A225485 and A325280.
%Y A325245 Cf. A008284, A047966, A116608, A127002, A181819, A182850, A323014, A323023, A325239, A325246, A325254, A325268, A325280.
%K A325245 nonn
%O A325245 0,6
%A A325245 _Gus Wiseman_, Apr 15 2019