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 A240058 #7 Apr 06 2014 04:17:14
%S A240058 1,0,1,0,3,1,4,2,8,5,12,9,21,17,32,29,52,49,79,79,123,126,184,195,278,
%T A240058 299,409,449,603,668,874,979,1263,1423,1803,2045,2563,2916,3608,4121,
%U A240058 5056,5783,7029,8055,9725,11151,13366,15337,18285,20979,24871,28535
%N A240058 Number of partitions of n such that m(1) = m(3), where m = multiplicity.
%F A240058 a(n) = A182714(n+3) - A182714(n) = A240059(n+1) - A240059(n) for n >= 0.
%e A240058 a(6) counts these 4 partitions: 6, 42, 321, 222.
%t A240058 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 A240058 t2 = Table[Count[f[n], p_ /; Count[p, 1] <= Count[p, 3]], {n, 0, z}] (* A182714(n+3) *)
%t A240058 t3 = Table[Count[f[n], p_ /; Count[p, 1] == Count[p, 3]], {n, 0, z}] (* A240058 *)
%t A240058 t4 = Table[Count[f[n], p_ /; Count[p, 1] > Count[p, 3]], {n, 0, z}] (* A240059 *)
%t A240058 t5 = Table[Count[f[n], p_ /; Count[p, 1] >= Count[p, 3]], {n, 0, z}] (* A240059(n+1) *)
%Y A240058 Cf. A182714, A240059, A000041.
%K A240058 nonn,easy
%O A240058 1,5
%A A240058 _Clark Kimberling_, Mar 31 2014