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 A325271 #5 Apr 23 2019 09:21:03
%S A325271 1,1,1,1,2,1,3,4,6,8,11,11,19,44,53,63,83,113,124,171,190,344,429,525,
%T A325271 662,796,981,1182,1442,1709,2096,2663,3406,4315,5426,6784,8417,10466,
%U A325271 12824,15721,19104,23267,27981,5,14,36,76,143,269,446,738,1143,1754
%N A325271 Number of integer partitions of n with frequency depth round(sqrt(n)).
%C A325271 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).
%e A325271 The a(2) = 1 through a(10) = 11 partitions:
%e A325271 (2) (111) (22) (11111) (33) (43) (53) (54) (64)
%e A325271 (1111) (222) (52) (62) (63) (73)
%e A325271 (111111) (61) (71) (72) (82)
%e A325271 (421) (431) (81) (91)
%e A325271 (521) (432) (532)
%e A325271 (3311) (531) (541)
%e A325271 (621) (631)
%e A325271 (222111) (721)
%e A325271 (3322)
%e A325271 (4321)
%e A325271 (4411)
%t A325271 fdadj[ptn_List]:=If[ptn=={},0,Length[NestWhileList[Sort[Length/@Split[#]]&,ptn,Length[#]>1&]]];
%t A325271 Table[Length[Select[IntegerPartitions[n],fdadj[#]==Round[Sqrt[n]]&]],{n,0,30}]
%Y A325271 Cf. A117571, A181819, A225485, A323014, A323023, A325245, A325246, A325272, A325253, A325258, A325278, A325280, A325282.
%K A325271 nonn
%O A325271 0,5
%A A325271 _Gus Wiseman_, Apr 23 2019