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 A241088 #7 May 11 2025 19:16:53
%S A241088 0,0,1,1,1,2,3,4,4,6,7,10,12,15,18,22,26,32,39,46,56,66,78,91,108,125,
%T A241088 147,171,200,231,269,309,357,410,470,538,616,703,801,913,1037,1178,
%U A241088 1335,1511,1707,1929,2172,2448,2752,3093,3470,3894,4359,4880,5455
%N A241088 Number of partitions p of n into distinct parts such that max(p) >= 2*(number of parts of p).
%e A241088 a(9) counts these 6 partitions: 9, 81, 72, 63, 621, 54.
%t A241088 z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241088 Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)
%t A241088 Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
%t A241088 Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
%t A241088 Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
%t A241088 Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)
%Y A241088 Cf. A241085, A241086, A241087, A241089.
%K A241088 nonn,easy
%O A241088 0,6
%A A241088 _Clark Kimberling_, Apr 17 2014