This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A240065 #5 Apr 06 2014 04:17:50
%S A240065 0,0,1,1,2,2,4,6,9,12,17,23,33,43,59,76,102,132,173,221,285,361,462,
%T A240065 580,733,913,1144,1418,1761,2168,2673,3273,4012,4885,5952,7212,8741,
%U A240065 10546,12719,15279,18344,21949,26247,31287,37268,44267,52541,62207,73584
%N A240065 Number of partitions of n such that m(2) > m(3), where m = multiplicity.
%F A240065 a(n) + A240063(n) + A240064(n) = A000041(n) for n >= 0.
%e A240065 a(6) counts these 4 partitions: 42, 222, 2211, 21111.
%t A240065 z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 2] < Count[p, 3]], {n, 0, z}] (* A240063 *)
%t A240065 t2 = Table[Count[f[n], p_ /; Count[p, 2] <= Count[p, 3]], {n, 0, z}] (* A240063(n+3) *)
%t A240065 t3 = Table[Count[f[n], p_ /; Count[p, 2] == Count[p, 3]], {n, 0, z}] (* A240064 *)
%t A240065 t4 = Table[Count[f[n], p_ /; Count[p, 2] > Count[p, 3]], {n, 0, z}] (* A240065 *)
%t A240065 t5 = Table[Count[f[n], p_ /; Count[p, 2] >= Count[p, 3]], {n, 0, z}] (* A240065(n+2) *)
%Y A240065 Cf. A240063, A240064, A182714, A000041.
%K A240065 nonn,easy
%O A240065 0,5
%A A240065 _Clark Kimberling_, Mar 31 2014