A241061 Number of partitions p of n into distinct parts such that max(p) < 1 + 2*min(p).

0, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 3, 4, 4, 4, 5, 4, 6, 7, 6, 6, 8, 8, 9, 10, 10, 10, 12, 12, 14, 16, 14, 16, 18, 18, 20, 22, 23, 24, 26, 26, 28, 32, 32, 35, 38, 38, 40, 44, 45, 48, 52, 54, 58, 62, 62, 66, 71, 74, 78, 84, 86, 92, 98, 100, 106, 112, 116, 122

Offset

0,4

Links

Table of n, a(n) for n=0..68.

Formula

a(n) + A241062(n) + A241064(n) = A000009(n) for n >= 1.

a(n) = A207642(n) - A241062(n) for n >= 0.

Example

a(10) counts these 2 partitions: {10}, {6,4}.

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 *)

Crossrefs

Cf. A207642, A241062, A241037, A241064, A000009.

Sequence in context: A077197 A320510 A117173 * A103858 A010554 A062610

Adjacent sequences: A241058 A241059 A241060 * A241062 A241063 A241064

Keyword

nonn,easy

Author

Clark Kimberling, Apr 16 2014

Status

approved