cp's OEIS Frontend

A241741 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 A241741 #5 May 06 2014 15:05:38
%S A241741 1,1,1,1,2,3,3,5,9,11,14,22,29,36,51,66,83,107,139,170,216,273,340,
%T A241741 415,520,635,778,952,1177,1414,1724,2094,2527,3038,3691,4411,5286,
%U A241741 6345,7586,9008,10778,12796,15163,17979,21288,25059,29608,34861,40927,48035
%N A241741 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 A241741 Each number in p is counted once, regardless of its multiplicity.
%F A241741 a(n) + A241740(n) + A241842(n) = A000041(n) for n >= 0.
%e A241741 a(8) counts these 9 partitions:  71, 62, 53, 44, 41111, 332, 3221, 32111, 11111111.
%t A241741 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241741 Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}]  (* A241740 *)
%t A241741 Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)
%t A241741 Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}]  (* A241742 *)
%Y A241741 Cf. A241737, A241740, A241742, A241743.
%K A241741 nonn,easy
%O A241741 0,5
%A A241741 _Clark Kimberling_, Apr 28 2014