cp's OEIS Frontend

A241745 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).

%I A241745 #5 May 06 2014 15:06:11
%S A241745 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 A241745 348,425,546,678,833,1041,1284,1558,1940,2351,2862,3496,4227,5093,
%U A241745 6187,7409,8920,10706,12795,15277,18259,21671,25803,30579,36218,42836,50596
%N A241745 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 A241745 Each number in p is counted once, regardless of its multiplicity.
%F A241745 a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
%e A241745 a(8) counts these 3 partitions:  62, 53, 332.
%t A241745 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241745 Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}]  (* A241743 *)
%t A241745 Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
%t A241745 Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}]  (* A241745 *)
%Y A241745 Cf. A241737, A241740, A241743, A241744.
%K A241745 nonn,easy
%O A241745 0,7
%A A241745 _Clark Kimberling_, Apr 28 2014