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%I #5 Apr 28 2014 18:50:57
%S 0,0,0,1,1,2,3,3,4,6,7,9,13,19,22,29,38,45,65,75,94,119,151,181,238,
%T 280,341,419,526,615,764,920,1097,1335,1605,1902,2285,2733,3233,3873,
%U 4586,5376,6386,7556,8845,10436,12234,14322,16812,19623,22806,26692
%N Number of partitions p of n such that the number of parts having multiplicity 1 is a part and max(p) - min(p) is a part.
%F a(n) + A241448(n) + A241449(n) = A241451(n) for n >= 0.
%e a(6) counts these 3 partitions: 42, 321, 21111.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Max[p]-Min[p]]], {n, 0, z}] (* A241447 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241448 *)
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241449 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241450 *)
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241451 *)
%Y Cf. A241448, A241449, A241450, A241451.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 23 2014
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