A240065 Number of partitions of n such that m(2) > m(3), where m = multiplicity.

0, 0, 1, 1, 2, 2, 4, 6, 9, 12, 17, 23, 33, 43, 59, 76, 102, 132, 173, 221, 285, 361, 462, 580, 733, 913, 1144, 1418, 1761, 2168, 2673, 3273, 4012, 4885, 5952, 7212, 8741, 10546, 12719, 15279, 18344, 21949, 26247, 31287, 37268, 44267, 52541, 62207, 73584

Offset: 0

Author

Clark Kimberling, Mar 31 2014

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A240063, A240064, A182714, A000041.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 2] < Count[p, 3]], {n, 0, z}]  (* A240063 *)
t2 = Table[Count[f[n], p_ /; Count[p, 2] <= Count[p, 3]], {n, 0, z}] (* A240063(n+3) *)
t3 = Table[Count[f[n], p_ /; Count[p, 2] == Count[p, 3]], {n, 0, z}] (* A240064 *)
t4 = Table[Count[f[n], p_ /; Count[p, 2] > Count[p, 3]], {n, 0, z}]  (* A240065 *)
t5 = Table[Count[f[n], p_ /; Count[p, 2] >= Count[p, 3]], {n, 0, z}] (* A240065(n+2) *)

Formula

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