cp's OEIS Frontend

A241740 Number of partitions p of n such that (number of numbers in p of form 3k+2) < (number of numbers in p of form 3k).

%I A241740 #5 May 06 2014 15:05:32
%S A241740 0,0,0,1,1,1,3,4,4,7,10,12,17,24,30,40,53,70,90,118,152,194,244,316,
%T A241740 396,497,626,784,960,1202,1483,1816,2230,2738,3312,4042,4908,5922,
%U A241740 7141,8627,10327,12388,14832,17703,21075,25120,29795,35321,41822,49439,58286
%N A241740 Number of partitions p of n such that (number of numbers in p of form 3k+2) < (number of numbers in p of form 3k).
%C A241740 Each number in p is counted once, regardless of its multiplicity.
%F A241740 a(n) + A241741(n) + A241842(n) = A000041(n) for n >= 0.
%e A241740 a(8) counts these 4 partitions:  611, 431, 3311, 311111.
%t A241740 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241740 Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}]  (* A241740 *)
%t A241740 Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)
%t A241740 Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}]  (* A241742 *)
%Y A241740 Cf. A241737, A241741, A241741, A241743.
%K A241740 nonn,easy
%O A241740 0,7
%A A241740 _Clark Kimberling_, Apr 28 2014