A241035 Number of partitions p of n into distinct parts such that max(p) = 2*min(p).

0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 0, 1, 3, 1, 0, 2, 1, 2, 3, 2, 1, 2, 2, 3, 5, 2, 2, 4, 3, 3, 5, 5, 5, 6, 3, 4, 7, 6, 7, 9, 7, 6, 9, 8, 8, 10, 10, 12, 14, 11, 11, 13, 13, 14, 17, 16, 17, 21, 18, 19, 22, 20, 21, 25, 25

Offset

0,10

Links

Table of n, a(n) for n=0..70.

Example

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

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, A241036, A241037.

Sequence in context: A297155 A037844 A037880 * A140698 A231599 A333290

Adjacent sequences: A241032 A241033 A241034 * A241036 A241037 A241038

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2014

Status

approved