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 A241552 #4 May 03 2014 16:53:23
%S A241552 0,0,0,0,1,1,2,3,5,8,12,17,23,34,47,64,87,115,154,204,266,346,444,573,
%T A241552 731,933,1174,1479,1855,2320,2884,3578,4411,5443,6678,8185,9977,12157,
%U A241552 14753,17886,21608,26058,31326,37631,45066,53911,64300,76609,91061
%N A241552 Number of partitions p of n such that (number of numbers of the form 5k + 3 in p) is a part of p.
%C A241552 Each number in p is counted once, regardless of its multiplicity.
%e A241552 a(6) counts these 2 partitions: 321, 3111.
%t A241552 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
%t A241552 Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241549 *)
%t A241552 Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241550 *)
%t A241552 Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241551 *)
%t A241552 Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}] (* A241552 *)
%t A241552 Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}] (* A241553 *)
%Y A241552 Cf. A241549, A241550, A241551, A241553.
%K A241552 nonn,easy
%O A241552 0,7
%A A241552 _Clark Kimberling_, Apr 26 2014