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%I #4 Apr 27 2014 10:24:31
%S 0,0,0,0,1,2,2,4,6,8,11,12,21,24,33,42,57,68,95,110,147,176,223,262,
%T 344,402,508,607,758,894,1117,1309,1614,1905,2315,2722,3306,3870,4657,
%U 5468,6536,7642,9113,10635,12608,14716,17346,20197,23770,27597,32334
%N Number of partitions p of n such that the number of parts is not a part and max(p) - min(p) is a part.
%F a(n) + A241382(n) + A241384(n) = A241386(n) for n >= 0.
%e a(9) counts these 8 partitions: 63, 3321, 32211, 321111, 22221, 222111, 221111, 2111111.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241382 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241383 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241384 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241385 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241386 *)
%Y Cf. A241382, A241384, A241385, A241386.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 21 2014
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