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%I #5 May 06 2014 15:06:11
%S 0,0,0,1,0,1,2,1,3,4,4,8,10,13,19,24,34,45,59,79,99,130,170,212,273,
%T 348,425,546,678,833,1041,1284,1558,1940,2351,2862,3496,4227,5093,
%U 6187,7409,8920,10706,12795,15277,18259,21671,25803,30579,36218,42836,50596
%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.
%F a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
%e a(8) counts these 3 partitions: 62, 53, 332.
%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, A241743, A241744.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Apr 28 2014
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