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%I #4 Apr 27 2014 10:25:10
%S 0,0,0,1,1,2,4,4,7,9,13,14,22,26,36,40,54,66,85,99,127,148,187,221,
%T 277,323,394,464,565,665,805,939,1126,1320,1573,1832,2183,2541,3004,
%U 3504,4111,4769,5614,6498,7599,8803,10256,11853,13783,15895,18429,21250
%N Number of partitions p of n such that the number of distinct parts is a part and max(p) - min(p) is a part.
%F a(n) + A241388(n) + A241389(n) = A241391(n) for n >= 0.
%e a(9) counts these 9 partitions: 432, 4311, 3321, 32211, 321111, 222211, 222111, 221111, 21111111.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241387 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241388 *)
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241389 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241390 *)
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241391 *)
%Y Cf. A241388, A241389, A241390, A241391.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 21 2014
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