A240867 - OEIS

%I #9 Jul 26 2024 04:57:58

%S 0,1,0,0,0,0,0,0,0,1,1,2,1,3,2,5,2,7,4,12,5,16,8,23,11,32,17,43,25,56,

%T 36,73,51,93,74,118,102,150,140,188,191,236,255,294,337,369,442,458,

%U 570,574,732,716,930,894,1174,1113,1467,1389,1830,1727,2259

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

%e a(13) counts these 3 partitions:  931, 841, 6421.

%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, A240866, A240868; for analogous sequences for unrestricted partitions, see A240573-A240579.

%K nonn,easy

%O 0,12

%A _Clark Kimberling_, Apr 14 2014