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%I #5 Apr 06 2014 04:17:41
%S 1,1,1,1,2,4,5,6,8,11,16,20,26,33,43,56,71,89,112,140,177,219,271,333,
%T 411,505,617,750,912,1105,1339,1612,1940,2327,2789,3334,3978,4733,
%U 5625,6670,7903,9338,11021,12980,15273,17940,21043,24640,28822,33661,39273
%N Number of partitions of n such that m(2) = m(3), where m = multiplicity.
%F A240063(n) + a(n) + A240065(n) = A000041(n) for n >= 0.
%e a(6) counts these 5 partitions: 6, 51, 411, 321, 222.
%t 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 t2 = Table[Count[f[n], p_ /; Count[p, 2] <= Count[p, 3]], {n, 0, z}] (* A240063(n+3) *)
%t t3 = Table[Count[f[n], p_ /; Count[p, 2] == Count[p, 3]], {n, 0, z}] (* A240064 *)
%t t4 = Table[Count[f[n], p_ /; Count[p, 2] > Count[p, 3]], {n, 0, z}] (* A240065 *)
%t t5 = Table[Count[f[n], p_ /; Count[p, 2] >= Count[p, 3]], {n, 0, z}] (* A240065(n+2) *)
%Y Cf. A240063, A240065, A182714, A000041.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Mar 31 2014
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