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%I #4 May 03 2014 11:32:19
%S 0,0,1,0,2,0,3,0,5,0,7,0,11,1,16,4,25,11,39,26,62,53,96,97,151,169,
%T 228,280,344,437,503,669,731,995,1034,1437,1463,2042,2014,2864,2780,
%U 3947,3780,5397,5139,7317,6913,9842,9340,13183,12519,17609,16859,23416
%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) = A241644(n) - A241643(n) for n >= 0.
%F a(n) + A241641(n) + A241643(n) = A000041(n) for n >= 0.
%e a(8) counts these 5 partitions: 8, 62, 44, 422, 2222.
%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, A241642, A241643, A241644.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 27 2014
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