A240499 - OEIS

%I #4 Apr 14 2014 11:14:06

%S 0,1,0,1,1,1,1,1,3,5,3,7,8,11,13,21,24,33,39,52,65,85,100,132,161,203,

%T 245,310,369,464,556,685,823,1008,1198,1465,1745,2103,2501,3009,3557,

%U 4261,5031,5987,7058,8370,9823,11613,13611,16014,18725,21974,25615

%N Number of partitions of n such that the multiplicity of the number of parts is a part.

%e a(9) counts these 5 partitions:  531, 51111, 4311, 4221, 333.

%t z = 60; f[n_] := f[n] = IntegerPartitions[n];

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Min[p]]]], {n, 0, z}]  (* A240496 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, (Min[p] + Max[p])/2]]], {n, 1, z}]  (* A240497 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]*Max[p]]]], {n, 0,  z}]  (* A240498 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Length[p]]]], {n, 0, z}]  (* A240499 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Length[p]]]], {n, 0, z}]  (* A240500 *)

%Y Cf. A240496, A240497, A240498, A240500.

%K nonn,easy

%O 0,9

%A _Clark Kimberling_, Apr 06 2014