cp's OEIS Frontend

A241744 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 A241744 #5 May 06 2014 15:06:04
%S A241744 1,0,1,0,2,2,3,6,7,10,17,18,27,36,44,61,76,93,124,151,193,241,297,369,
%T A241744 462,558,707,850,1044,1281,1561,1884,2323,2761,3367,4050,4857,5826,
%U A241744 7024,8307,9982,11840,14058,16684,19785,23265,27585,32379,38125,44760
%N A241744 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 A241744 Each number in p is counted once, regardless of its multiplicity.
%F A241744 a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
%e A241744 a(8) counts these 7 partitions:  8, 611, 3311, 3221, 32111, 311111, 2222.
%t A241744 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241744 Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}]  (* A241743 *)
%t A241744 Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
%t A241744 Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}]  (* A241745 *)
%Y A241744 Cf. A241737, A241740, A241743, A241745.
%K A241744 nonn,easy
%O A241744 1,5
%A A241744 _Clark Kimberling_, Apr 28 2014