cp's OEIS Frontend

A241737 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 A241737 #6 May 06 2014 15:04:50
%S A241737 0,0,1,0,1,2,1,2,6,3,8,14,11,20,35,31,51,77,75,113,166,168,241,333,
%T A241737 351,482,651,697,935,1223,1339,1745,2251,2486,3190,4030,4499,5675,
%U A241737 7101,7960,9930,12244,13821,17011,20817,23532,28737,34795,39466,47727,57427
%N A241737 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 A241737 Each number in p is counted once, regardless of its multiplicity.
%F A241737 a(n) + A241738(n) + A241839(n) = A000041(n) for n >= 0.
%e A241737 a(8) counts these 6 partitions:  8, 61, 53, 521, 332, 2222.
%t A241737 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241737 Table[Count[f[n], p_ /; s[1, p] < s[2, p]], {n, 0, z}]  (* A241737 *)
%t A241737 Table[Count[f[n], p_ /; s[1, p] == s[2, p]], {n, 0, z}] (* A241738 *)
%t A241737 Table[Count[f[n], p_ /; s[1, p] > s[2, p]], {n, 0, z}]  (* A241739 *)
%Y A241737 Cf. A241738, A241739, A241740, A241743.
%K A241737 nonn,easy
%O A241737 0,6
%A A241737 _Clark Kimberling_, Apr 28 2014