A240866 - OEIS

%I #9 Jul 26 2024 06:41:11

%S 0,0,0,0,0,0,1,0,2,1,3,2,4,3,5,6,6,8,8,13,10,18,14,26,19,34,26,47,37,

%T 59,50,77,70,98,95,125,129,157,171,198,230,247,299,310,391,388,503,

%U 483,647,604,816,754,1034,939,1291,1172,1610,1458,1989,1813,2454

%N Number of partitions of n into distinct parts of which the number of even parts is a part and the number of odd parts is not a part.

%e a(10) counts these 3 partitions:  82, 631, 541.

%t z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

%t     t1 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240862 *)

%t     t2 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240863, *)

%t     t3 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240864 *)

%t     t4 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240865 *)

%t     t5 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240866 *)

%t     t6 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240867 *)

%t     t7 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240868 *)

%Y Cf. A240862, A240863, A240864, A240865, A240867, A240868; for analogous sequences for unrestricted partitions, see A240573-A240579.

%K nonn,easy

%O 0,9

%A _Clark Kimberling_, Apr 14 2014