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%I #5 May 03 2014 11:32:49
%S 0,1,1,3,3,7,8,14,16,26,32,45,57,78,103,132,175,221,299,366,491,599,
%T 803,962,1278,1528,2014,2391,3109,3681,4749,5596,7132,8401,10602,
%U 12445,15554,18244,22600,26468,32493,38025,46346,54164,65522,76549,92009,107375
%N Number of partitions p of n such that (number of even numbers in p) < 2*(number of odd numbers in p).
%C Each number in p is counted once, regardless of its multiplicity.
%F a(n) = A241642(n) - A241643(n) for n >= 0.
%F a(n) + A241643(n) + A241645(n) = A000041(n) for n >= 0.
%e a(6) counts these 8 partitions: 51, 411, 33, 321, 3111, 2211, 21111, 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_ /; s0[p] < 2 s1[p]], {n, 0, z}] (* A241641 *)
%t Table[Count[f[n], p_ /; s0[p] <= 2 s1[p]], {n, 0, z}] (* A241642 *)
%t Table[Count[f[n], p_ /; s0[p] == 2 s1[p]], {n, 0, z}] (* A241643 *)
%t Table[Count[f[n], p_ /; s0[p] >= 2 s1[p]], {n, 0, z}] (* A241644 *)
%t Table[Count[f[n], p_ /; s0[p] > 2 s1[p]], {n, 0, z}] (* A241645 *)
%Y Cf. A241642, A241643, A241644, A241645.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 27 2014
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