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 A241553 #4 May 03 2014 16:53:29
%S A241553 0,0,0,0,0,1,1,2,3,5,8,12,17,25,33,49,65,90,119,159,210,277,358,466,
%T A241553 593,766,968,1231,1548,1942,2427,3026,3747,4642,5704,7022,8587,10498,
%U A241553 12775,15519,18799,22730,27394,32981,39558,47426,56676,67650,80564,95781
%N A241553 Number of partitions p of n such that (number of numbers of the form 5k + 4 in p) is a part of p.
%C A241553 Each number in p is counted once, regardless of its multiplicity.
%e A241553 a(6) counts this single partition: 411.
%t A241553 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
%t A241553 Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241549 *)
%t A241553 Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241550 *)
%t A241553 Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241551 *)
%t A241553 Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}] (* A241552 *)
%t A241553 Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}] (* A241553 *)
%Y A241553 Cf. A241549, A241550, A241551, A241552.
%K A241553 nonn,easy
%O A241553 0,8
%A A241553 _Clark Kimberling_, Apr 26 2014