|
%I #4 Apr 22 2014 01:30:19
%S 0,1,0,1,0,1,1,2,1,3,3,5,4,7,7,11,10,15,15,22,22,31,31,42,43,58,59,78,
%T 82,105,109,139,146,183,193,239,255,311,331,402,430,516,553,659,710,
%U 839,904,1061,1146,1337,1446,1679,1819,2099,2276,2615,2838,3246
%N Number of partitions of n into distinct parts of which the number of odd parts is a part.
%F a(n) + A240870(n) = A000009(n) for n >= 0.
%e a(10) counts these 3 partitions: 721, 532, 4321.
%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, A240864, A240865, A240866, A240867, A204868; for analogous sequences for unrestricted partitions, see A240573-A240579.
%K nonn,easy
%O 0,8
%A _Clark Kimberling_, Apr 14 2014
|
