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%I #4 May 03 2014 11:32:41
%S 1,1,1,3,3,7,8,15,17,30,35,56,66,100,119,172,206,286,346,464,565,739,
%T 906,1158,1424,1789,2208,2730,3374,4128,5101,6173,7618,9148,11276,
%U 13446,16514,19595,24001,28321,34558,40636,49394,57864,70036,81817,98645,114912
%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) = A241641(n) + A241643(n) for n >= 0.
%F a(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]; 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. A241641, A241643, A241644, A241645.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 27 2014
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