cp's OEIS Frontend

A241739 Number of partitions p of n such that (number of numbers in p of form 3k+1) > (number of numbers in p of form 3k+2).

%I A241739 #5 May 06 2014 15:04:42
%S A241739 0,1,1,1,3,3,3,8,9,10,20,24,27,49,58,69,109,132,153,234,279,331,469,
%T A241739 565,662,918,1093,1290,1723,2056,2411,3165,3751,4411,5656,6700,7839,
%U A241739 9932,11707,13699,17084,20099,23441,28939,33914,39498,48236,56392,65481
%N A241739 Number of partitions p of n such that (number of numbers in p of form 3k+1) > (number of numbers in p of form 3k+2).
%C A241739 Each number in p is counted once, regardless of its multiplicity.
%F A241739 a(n) + A241737(n) + A241838(n) = A000041(n) for n >= 0.
%e A241739 a(8) counts these 9 partitions: 71, 611, 44, 431, 4211, 3311, 311111, 11111111.
%t A241739 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241739 Table[Count[f[n], p_ /; s[1, p] < s[2, p]], {n, 0, z}]  (* A241737 *)
%t A241739 Table[Count[f[n], p_ /; s[1, p] == s[2, p]], {n, 0, z}] (* A241738 *)
%t A241739 Table[Count[f[n], p_ /; s[1, p] > s[2, p]], {n, 0, z}]  (* A241739 *)
%Y A241739 Cf. A241737, A241738, A241740, A241743.
%K A241739 nonn,easy
%O A241739 0,5
%A A241739 _Clark Kimberling_, Apr 28 2014