A240540 - OEIS

%I #4 Apr 17 2014 14:29:20

%S 0,0,0,1,2,2,2,5,7,8,13,17,26,31,43,55,76,98,125,161,206,261,331,417,

%T 518,648,805,995,1229,1508,1848,2255,2751,3335,4044,4884,5892,7084,

%U 8510,10183,12179,14524,17299,20555,24398,28885,34169,40337,47551,55961

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

%e a(7) counts these 5 partitions:  61, 421, 322, 3211, 22111; e.g., 421 has 2 even parts, and the multiplicity of 2 is 1, which is a part of 421.

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

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 0]]]], {n, 0, z}]  (* A240540 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 1]]]], {n, 0, z}]  (* A240541 *)

%Y Cf. A240541.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 07 2014