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%I #4 May 03 2014 16:53:29
%S 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 593,766,968,1231,1548,1942,2427,3026,3747,4642,5704,7022,8587,10498,
%U 12775,15519,18799,22730,27394,32981,39558,47426,56676,67650,80564,95781
%N Number of partitions p of n such that (number of numbers of the form 5k + 4 in p) is a part of p.
%C Each number in p is counted once, regardless of its multiplicity.
%e a(6) counts this single partition: 411.
%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, A241551, A241552.
%K nonn,easy
%O 0,8
%A _Clark Kimberling_, Apr 26 2014
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