A240065 - OEIS

%I #5 Apr 06 2014 04:17:50

%S 0,0,1,1,2,2,4,6,9,12,17,23,33,43,59,76,102,132,173,221,285,361,462,

%T 580,733,913,1144,1418,1761,2168,2673,3273,4012,4885,5952,7212,8741,

%U 10546,12719,15279,18344,21949,26247,31287,37268,44267,52541,62207,73584

%N Number of partitions of n such that m(2) > m(3), where m = multiplicity.

%F a(n) + A240063(n) + A240064(n) = A000041(n) for n >= 0.

%e a(6) counts these 4 partitions:  42, 222, 2211, 21111.

%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, A240064, A182714, A000041.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Mar 31 2014