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A241640 Number of partitions p of n such that (number of even numbers in p) > (number of odd numbers in p).

%I A241640 #7 May 19 2014 10:42:17
%S A241640 0,0,1,0,2,0,3,1,6,4,10,11,20,23,32,44,57,77,90,129,150,208,236,334,
%T A241640 381,522,595,803,936,1234,1435,1861,2193,2770,3291,4105,4884,6001,
%U A241640 7172,8678,10418,12487,14969,17791,21330,25164,30181,35398,42337,49463,59057
%N A241640 Number of partitions p of n such that (number of even numbers in p) > (number of odd numbers in p).
%C A241640 Each number in p is counted once, regardless of its multiplicity.
%H A241640 Alois P. Heinz, <a href="/A241640/b241640.txt">Table of n, a(n) for n = 0..1000</a>
%F A241640 a(n) = A241639(n) - A241638(n) for n >= 0.
%F A241640 a(n) + A241636(n) + A241638(n) = A000041(n) for n >= 0.
%F A241640 a(n) = Sum_{k<0} A242618(n,k). - _Alois P. Heinz_, May 19 2014
%e A241640 a(6) counts these 3 partitions:  6, 42, 222.
%t A241640 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2],   0];
%t A241640 s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];
%t A241640 Table[Count[f[n], p_ /; s0[p] < s1[p]], {n, 0, z}]  (* A241636 *)
%t A241640 Table[Count[f[n], p_ /; s0[p] <= s1[p]], {n, 0, z}] (* A241637 *)
%t A241640 Table[Count[f[n], p_ /; s0[p] == s1[p]], {n, 0, z}] (* A241638 *)
%t A241640 Table[Count[f[n], p_ /; s0[p] >= s1[p]], {n, 0, z}] (* A241639 *)
%t A241640 Table[Count[f[n], p_ /; s0[p] > s1[p]], {n, 0, z}]  (* A241640 *)
%Y A241640 Cf. A241636, A241637, A241638, A241639.
%K A241640 nonn,easy
%O A241640 0,5
%A A241640 _Clark Kimberling_, Apr 27 2014