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%I #10 Apr 07 2016 19:13:35
%S 0,1,1,2,3,4,6,8,12,16,21,30,40,52,72,91,121,159,202,260,335,421,535,
%T 674,840,1052,1304,1614,1996,2451,3002,3674,4468,5442,6592,7971,9624,
%U 11584,13898,16691,19947,23823,28410,33782,40113,47610,56302,66572,78569
%N Number of partitions p of n such that (number of numbers in p of form 3k) < (number of numbers in p of form 3k+1).
%C Each number in p is counted once, regardless of its multiplicity.
%H Alois P. Heinz, <a href="/A241743/b241743.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
%e a(8) counts these 12 partitions: 71, 521, 5111, 44, 431, 422, 4211, 41111, 22211, 221111, 2111111, 11111111.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}] (* A241743 *)
%t Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
%t Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}] (* A241745 *)
%Y Cf. A241737, A241740, A241744, A241745.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 28 2014
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