cp's OEIS Frontend

A241742 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 A241742 #5 May 06 2014 15:05:53
%S A241742 0,0,1,1,2,3,5,6,9,12,18,22,31,41,54,70,95,120,156,202,259,325,418,
%T A241742 524,659,826,1032,1274,1581,1949,2397,2932,3592,4367,5307,6430,7783,
%U A241742 9370,11288,13550,16233,19399,23179,27579,32812,38955,46155,54572,64524,76051
%N A241742 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 A241742 Each number in p is counted once, regardless of its multiplicity.
%F A241742 a(n) + A241740(n) + A241841(n) = A000041(n) for n >= 0.
%e A241742 a(8) counts these 9 partitions:  8, 521, 5111, 422, 4211, 2222, 22211, 221111, 2111111.
%t A241742 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241742 Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}]  (* A241740 *)
%t A241742 Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)
%t A241742 Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}]  (* A241742 *)
%Y A241742 Cf. A241737, A241740, A241741, A241743.
%K A241742 nonn,easy
%O A241742 0,5
%A A241742 _Clark Kimberling_, Apr 28 2014