A241062 Number of partitions p of n into distinct parts such that max(p) = 1 + 2*min(p).

0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 1, 2, 0, 1, 3, 2, 2, 2, 1, 2, 4, 4, 2, 3, 2, 3, 6, 4, 4, 6, 4, 4, 5, 6, 8, 8, 7, 6, 8, 7, 8, 12, 10, 10, 13, 12, 11, 12, 12, 14, 18, 18, 17, 18, 18, 18, 22, 20, 22, 26, 25, 28, 30, 29, 30, 32

Offset: 0

Author

Clark Kimberling, Apr 16 2014

Keywords

• nonn
• easy

Examples

			a(10) counts these 2 partitions:  73, 532.
		

Crossrefs

Cf. A207642, A241061, A241037, A241064, A000009.

Programs

Mathematica

z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
  Table[Count[f[n], p_ /; Max[p] < 1 + 2*Min[p]], {n, 0, z}] (* A241061 *)
  Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}](* A207642 *)
  Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}](* A241062 *)
  Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}](* A241037 *)
  Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}] (* A241064 *)

Formula

a(n) + A241061(n) + A241064(n) = A000009(n) for n >= 1.

a(n) = A241037(n) - A241064(n) = A207642(n) - A241061(n) for n >= 0.