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%I #4 May 03 2014 11:31:44
%S 1,1,1,2,2,3,5,6,10,13,21,25,40,47,69,84,117,138,187,222,292,344,439,
%T 519,654,768,951,1118,1378,1612,1968,2308,2807,3282,3977,4657,5630,
%U 6585,7936,9278,11170,13046,15648,18274,21868,25481,30402,35385,42069,48875
%N Number of partitions p of n such that 2*(number of even numbers in p) <= (number of odd numbers in p).
%C Each number in p is counted once, regardless of its multiplicity.
%F a(n) = A241651(n) + A241653(n) for n >= 0.
%F a(n) + A241655(n) = A000041(n) for n >= 0.
%e a(6) counts these 5 partitions: 51, 33, 321, 3111, 111111.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0];
%t s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];
%t Table[Count[f[n], p_ /; 2 s0[p] < s1[p]], {n, 0, z}] (* A241651 *)
%t Table[Count[f[n], p_ /; 2 s0[p] <= s1[p]], {n, 0, z}] (* A241652 *)
%t Table[Count[f[n], p_ /; 2 s0[p] == s1[p]], {n, 0, z}] (* A241653 *)
%t Table[Count[f[n], p_ /; 2 s0[p] >= s1[p]], {n, 0, z}] (* A241654 *)
%t Table[Count[f[n], p_ /; 2 s0[p] > s1[p]], {n, 0, z}] (* A241655 *)
%Y Cf. A241651, A241653, A241654, A241655.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 27 2014
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