A241389 - OEIS

%I #4 Apr 27 2014 10:25:31

%S 0,1,1,1,1,2,1,3,3,5,6,10,13,17,25,34,46,61,80,108,141,182,236,307,

%T 376,499,618,783,970,1233,1491,1884,2306,2841,3452,4277,5128,6299,

%U 7574,9176,11046,13333,15882,19114,22803,27154,32308,38435,45476,53904,63628

%N Number of partitions p of n such that the number of distinct parts is a part and max(p) - min(p) is not a part.

%F a(n) + A241387(n) + A241388(n) = A241391(n) for n >= 0.

%e a(9) counts these 5 partitions:  72, 531, 522, 3222, 111111111.

%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. A241387, A241388, A241390, A241391.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 21 2014