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A241639 Number of partitions p of n such that (number of even numbers in p) >= (number of odd numbers in p).

%I A241639 #7 May 19 2014 10:42:45
%S A241639 1,0,1,1,3,4,6,9,12,17,21,31,37,54,66,91,113,155,193,254,317,411,517,
%T A241639 649,814,1009,1268,1548,1925,2335,2907,3484,4309,5156,6343,7535,9231,
%U A241639 10949,13340,15782,19091,22555,27179,32025,38377,45171,53852,63267,75076
%N A241639 Number of partitions p of n such that (number of even numbers in p) >= (number of odd numbers in p).
%C A241639 Each number in p is counted once, regardless of its multiplicity.
%H A241639 Alois P. Heinz, <a href="/A241639/b241639.txt">Table of n, a(n) for n = 0..1000</a>
%F A241639 a(n) = A241638(n) + A241640(n) for n >= 0.
%F A241639 a(n) + A241636(n) = A000041(n) for n >= 0.
%F A241639 a(n) = Sum_{k<=0} A242618(n,k). - _Alois P. Heinz_, May 19 2014
%e A241639 a(6) counts these 6 partitions:  6, 42, 411, 222, 2211, 21111.
%t A241639 z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2],   0];
%t A241639 s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];
%t A241639 Table[Count[f[n], p_ /; s0[p] < s1[p]], {n, 0, z}]  (* A241636 *)
%t A241639 Table[Count[f[n], p_ /; s0[p] <= s1[p]], {n, 0, z}] (* A241637 *)
%t A241639 Table[Count[f[n], p_ /; s0[p] == s1[p]], {n, 0, z}] (* A241638 *)
%t A241639 Table[Count[f[n], p_ /; s0[p] >= s1[p]], {n, 0, z}] (* A241639 *)
%t A241639 Table[Count[f[n], p_ /; s0[p] > s1[p]], {n, 0, z}]  (* A241640 *)
%Y A241639 Cf. A241636, A241637, A241638, A241640.
%K A241639 nonn,easy
%O A241639 0,5
%A A241639 _Clark Kimberling_, Apr 27 2014