A241067 Number of partitions p of n into distinct parts such that max(p) = -1 + 2*min(p).

0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 2, 3, 1, 1, 4, 2, 3, 4, 3, 3, 3, 3, 4, 6, 5, 4, 6, 4, 5, 7, 6, 7, 8, 8, 8, 9, 7, 8, 11, 11, 11, 13, 12, 12, 15, 12, 14, 17, 15, 18, 19, 20, 20

Offset

0,18

Links

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

Example

a(17) counts these 2 partitions:  {11,6}, {7,6,4}.

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}]  (* A241065 *)
Table[Count[f[n], p_ /; Max[p] <= -1 + 2*Min[p]], {n, 0, z}] (* A240874 *)
Table[Count[f[n], p_ /; Max[p] == -1 + 2*Min[p]], {n, 0, z}] (* A241067 *)
Table[Count[f[n], p_ /; Max[p] >= -1 + 2*Min[p]], {n, 0, z}] (* A241068 *)
Table[Count[f[n], p_ /; Max[p] > -1 + 2*Min[p]], {n, 0, z}]  (* A241036 *)

Crossrefs

Cf. A241065, A240874, A241068, A241036.

Sequence in context: A281640 A281452 A341023 * A130457 A130454 A070787

Adjacent sequences: A241064 A241065 A241066 * A241068 A241069 A241070

Keyword

nonn,easy

Author

Clark Kimberling, Apr 16 2014

Status

approved