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 A325253 #4 Apr 23 2019 09:20:47
%S A325253 1,1,1,1,2,2,4,4,6,8,17,26,25,44,53,63,83,128,168,212,273,344,429,525,
%T A325253 662,796,684,910,1211,1595,2060,2663,3406,4315,5426,6784,8417,0,0,0,0,
%U A325253 0,1,5,14,36,76,143,269,446,0,0,0,0,0,0,0,0,0,0,0
%N A325253 Number of integer partitions of n with adjusted frequency depth ceiling(sqrt(n)).
%C A325253 The adjusted frequency depth of an integer partition is 0 if the partition is empty, and otherwise it is one 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 A325253 The a(2) = 1 through a(11) = 26 partitions:
%e A325253 11 111 22 32 42 43 53 54 433 443
%e A325253 1111 41 51 52 62 63 442 533
%e A325253 321 61 71 72 622 551
%e A325253 2211 421 431 81 811 722
%e A325253 521 432 3331 911
%e A325253 3311 531 4222 3332
%e A325253 621 7111 5222
%e A325253 222111 61111 8111
%e A325253 222211 32222
%e A325253 322111 33311
%e A325253 331111 44111
%e A325253 511111 71111
%e A325253 2221111 222221
%e A325253 4111111 322211
%e A325253 22111111 332111
%e A325253 31111111 422111
%e A325253 211111111 611111
%e A325253 2222111
%e A325253 3221111
%e A325253 3311111
%e A325253 5111111
%e A325253 22211111
%e A325253 41111111
%e A325253 221111111
%e A325253 311111111
%e A325253 2111111111
%t A325253 fdadj[ptn_List]:=If[ptn=={},0,Length[NestWhileList[Sort[Length/@Split[#1]]&,ptn,Length[#1]>1&]]];
%t A325253 Table[Length[Select[IntegerPartitions[n],fdadj[#]==Ceiling[Sqrt[n]]&]],{n,0,30}]
%Y A325253 Cf. A117571, A181819, A225485, A323014, A323023, A325245, A325246, A325252, A325258, A325271, A325278, A325280, A325282.
%K A325253 nonn
%O A325253 0,5
%A A325253 _Gus Wiseman_, Apr 22 2019