A241037 Number of partitions p of n into distinct parts such that max(p) > 2*min(p).

0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 8, 9, 11, 14, 18, 22, 28, 32, 39, 48, 58, 68, 81, 95, 112, 132, 155, 180, 210, 242, 280, 326, 374, 430, 494, 565, 646, 737, 840, 956, 1087, 1232, 1394, 1578, 1781, 2010, 2266, 2550, 2866, 3219, 3610, 4045, 4528, 5062, 5656, 6316

Offset: 0

Author

Clark Kimberling, Apr 15 2014

Keywords

• nonn
• easy

Examples

			a(9) counts these 4 partitions:  {8,1}, {7,2}, {6,2,1}, {5,3,1}.
		

Crossrefs

Cf. A240874, A241035, A241036.

Programs

Mathematica

z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 2*Min[p]], {n, 0, z}]  (* A240874 *)
Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)
Table[Count[f[n], p_ /; Max[p] >= 2*Min[p]], {n, 0, z}] (* A241036 *)
Table[Count[f[n], p_ /; Max[p] > 2*Min[p]], {n, 0, z}]  (* A241037 *)