A241449 - OEIS

%I #5 Apr 28 2014 18:54:22

%S 0,1,0,0,0,2,2,5,6,11,14,20,25,40,46,71,86,125,149,213,257,351,425,

%T 562,683,896,1089,1397,1688,2138,2600,3256,3918,4880,5873,7218,8681,

%U 10618,12683,15428,18396,22242,26460,31798,37670,45134,53364,63520,74918

%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 not a part.

%F a(n) + A241447(n) + A241448(n) = A241451(n) for n >= 0.

%e a(6) counts these 2 partitions:  411, 3111.

%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, A241448, A241450, A241451.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 23 2014