A241036 Number of partitions p of n into distinct parts such that max(p) >= 2*min(p).

0, 0, 0, 1, 1, 1, 3, 3, 4, 6, 8, 9, 12, 15, 19, 23, 28, 33, 42, 49, 58, 70, 82, 97, 115, 134, 156, 182, 212, 245, 285, 328, 376, 434, 497, 568, 651, 742, 845, 962, 1090, 1236, 1401, 1584, 1788, 2019, 2273, 2556, 2875, 3227, 3618, 4055, 4538, 5074, 5670, 6327

Offset

0,7

Links

Table of n, a(n) for n=0..55.

Example

a(11) counts these 9 partitions:  {10,1}, {9,2}, {8,3}, {8,2,1}, {7,3,1}, {6,4,1}, {6,3,2}, {5,4,2}, {5,3,2,1}.

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 *)

Crossrefs

Cf. A240874, A241035, A241037.

Sequence in context: A023837 A240115 A196249 * A241050 A363237 A080013

Adjacent sequences: A241033 A241034 A241035 * A241037 A241038 A241039

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2014

Status

approved