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 A241551 #4 May 03 2014 16:53:17
%S A241551 0,0,0,1,1,2,3,5,8,13,16,25,34,49,66,90,119,161,211,279,357,465,595,
%T A241551 764,968,1224,1536,1933,2406,2999,3703,4577,5628,6910,8441,10295,
%U A241551 12507,15184,18356,22163,26661,32035,38395,45937,54821,65321,77655,92209,109242
%N A241551 Number of partitions p of n such that (number of numbers of the form 5k + 2 in p) is a part of p.
%C A241551 Each number in p is counted once, regardless of its multiplicity.
%e A241551 a(6) counts these 3 partitions: 321, 2211, 21111.
%t A241551 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
%t A241551 Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241549 *)
%t A241551 Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241550 *)
%t A241551 Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241551 *)
%t A241551 Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}] (* A241552 *)
%t A241551 Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}] (* A241553 *)
%Y A241551 Cf. A241549, A241550, A241552, A241553.
%K A241551 nonn,easy
%O A241551 0,6
%A A241551 _Clark Kimberling_, Apr 26 2014