A241448 - OEIS

%I #5 Apr 28 2014 18:52:29

%S 0,0,0,0,0,0,1,1,3,4,7,6,14,9,21,21,31,35,50,52,82,85,117,129,174,191,

%T 265,291,366,427,547,597,788,868,1087,1244,1549,1726,2159,2420,2954,

%U 3405,4108,4630,5637,6396,7640,8744,10359,11822,14087,15989,18779

%N Number of partitions p of n such that the number of parts having multiplicity 1 is not a part and max(p) - min(p) is a part.

%F a(n) + A241447(n) + A241449(n) = A241451(n) for n >= 0.

%e a(6) counts this single partition:  2211.

%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. A241447, A241449, A241450, A241451.

%K nonn,easy

%O 0,9

%A _Clark Kimberling_, Apr 23 2014