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 A240059 #6 Apr 06 2014 04:17:25
%S A240059 0,1,1,2,2,5,6,10,12,20,25,37,46,67,84,116,145,197,246,325,404,527,
%T A240059 653,837,1032,1310,1609,2018,2467,3070,3738,4612,5591,6854,8277,10080,
%U A240059 12125,14688,17604,21212,25333,30389,36172,43201,51256,60981,72132,85498
%N A240059 Number of partitions of n such that m(1) > m(3), where m = multiplicity.
%F A240059 a(n) + A182714(n) + A240058(n) = A000041(n) for n >= 0.
%e A240059 a(6) counts these 6 partitions: 51, 411, 3111, 2211, 21111, 111111.
%t A240059 z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 1] < Count[p, 3]], {n, 0, z}] (* A182714 *)
%t A240059 t2 = Table[Count[f[n], p_ /; Count[p, 1] <= Count[p, 3]], {n, 0, z}] (* A182714(n+3) *)
%t A240059 t3 = Table[Count[f[n], p_ /; Count[p, 1] == Count[p, 3]], {n, 0, z}] (* A240058 *)
%t A240059 t4 = Table[Count[f[n], p_ /; Count[p, 1] > Count[p, 3]], {n, 0, z}] (* A240059 *)
%t A240059 t5 = Table[Count[f[n], p_ /; Count[p, 1] >= Count[p, 3]], {n, 0, z}] (* A240059(n+1) *)
%Y A240059 Cf. A182714, A240058, A000041.
%K A240059 nonn,easy
%O A240059 0,4
%A A240059 _Clark Kimberling_, Mar 31 2014