A240578 - OEIS

%I #4 Apr 17 2014 14:30:01

%S 0,1,0,0,0,1,0,2,2,6,3,8,9,18,15,27,33,48,55,73,101,122,162,183,272,

%T 293,421,436,666,670,1002,989,1522,1483,2237,2152,3303,3155,4762,4521,

%U 6874,6498,9754,9188,13825,12995,19345,18139,27013,25297,37332,34909

%N Number of partitions of n such that the number of odd parts is a part and the number of even parts is not a part.

%e a(9) counts these 6 partitions:  531, 51111, 441, 4221, 333, 22221.

%t z = 62; f[n_] := f[n] = IntegerPartitions[n];

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}]  (* A240573 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240574 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240575 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240576 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240577 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240578 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240579 *)

%Y Cf. A240573, A240574, A240575, A240576, A240577, A240579.

%K nonn,easy

%O 0,8

%A _Clark Kimberling_, Apr 10 2014