A241088 Number of partitions p of n into distinct parts such that max(p) >= 2*(number of parts of p).

0, 0, 1, 1, 1, 2, 3, 4, 4, 6, 7, 10, 12, 15, 18, 22, 26, 32, 39, 46, 56, 66, 78, 91, 108, 125, 147, 171, 200, 231, 269, 309, 357, 410, 470, 538, 616, 703, 801, 913, 1037, 1178, 1335, 1511, 1707, 1929, 2172, 2448, 2752, 3093, 3470, 3894, 4359, 4880, 5455

Offset

0,6

Links

Table of n, a(n) for n=0..54.

Example

a(9) counts these 6 partitions:  9, 81, 72, 63, 621, 54.

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}]  (* A241085 *)
Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}]  (* A241089 *)

Crossrefs

Cf. A241085, A241086, A241087, A241089.

Sequence in context: A007896 A351006 A325682 * A074139 A355026 A238963

Adjacent sequences: A241085 A241086 A241087 * A241089 A241090 A241091

Keyword

nonn,easy

Author

Clark Kimberling, Apr 17 2014

Status

approved