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 A241089 #7 May 11 2025 19:16:39
%S A241089 0,0,0,1,1,1,2,3,4,5,6,8,10,13,16,20,24,29,35,42,50,61,72,85,101,118,
%T A241089 138,161,188,218,254,293,339,391,450,515,591,675,771,878,999,1135,
%U A241089 1289,1460,1652,1868,2108,2376,2676,3009,3379,3793,4250,4760,5325,5952
%N A241089 Number of partitions p of n into distinct parts such that max(p) > 2*(number of parts of p).
%e A241089 a(9) counts these 5 partitions: 9, 81, 72, 63, 54.
%t A241089 z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241089 Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)
%t A241089 Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
%t A241089 Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
%t A241089 Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
%t A241089 Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)
%Y A241089 Cf. A241085, A241086, A241087, A241088.
%K A241089 nonn,easy
%O A241089 0,7
%A A241089 _Clark Kimberling_, Apr 17 2014