|
%I #6 Apr 22 2014 01:31:03
%S 0,0,1,1,2,2,2,3,3,4,4,5,7,8,10,10,16,15,23,19,32,27,44,36,60,50,80,
%T 67,103,92,137,124,174,167,224,221,284,292,362,382,453,497,574,641,
%U 715,821,897,1046,1117,1323,1396,1664,1729,2082,2151,2591,2660,3213
%N Number of partitions of n into distinct parts of which the number of even parts is not a part and the number of odd parts is not a part.
%e a(9) counts these 4 partitions: 9, 72, 63, 54.
%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, A204867; for analogous sequences for unrestricted partitions, see A240573-A240579.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 14 2014
|
