cp's OEIS Frontend

A241743 Number of partitions p of n such that (number of numbers in p of form 3k) < (number of numbers in p of form 3k+1).

%I A241743 #10 Apr 07 2016 19:13:35
%S A241743 0,1,1,2,3,4,6,8,12,16,21,30,40,52,72,91,121,159,202,260,335,421,535,
%T A241743 674,840,1052,1304,1614,1996,2451,3002,3674,4468,5442,6592,7971,9624,
%U A241743 11584,13898,16691,19947,23823,28410,33782,40113,47610,56302,66572,78569
%N A241743 Number of partitions p of n such that (number of numbers in p of form 3k) < (number of numbers in p of form 3k+1).
%C A241743 Each number in p is counted once, regardless of its multiplicity.
%H A241743 Alois P. Heinz, <a href="/A241743/b241743.txt">Table of n, a(n) for n = 0..1000</a>
%F A241743 a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
%e A241743 a(8) counts these 12 partitions: 71, 521, 5111, 44, 431, 422, 4211, 41111, 22211, 221111, 2111111, 11111111.
%t A241743 z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
%t A241743 Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}]  (* A241743 *)
%t A241743 Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
%t A241743 Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}]  (* A241745 *)
%Y A241743 Cf. A241737, A241740, A241744, A241745.
%K A241743 nonn,easy
%O A241743 0,4
%A A241743 _Clark Kimberling_, Apr 28 2014