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