A241089 Number of partitions p of n into distinct parts such that max(p) > 2*(number of parts of p).

0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, 24, 29, 35, 42, 50, 61, 72, 85, 101, 118, 138, 161, 188, 218, 254, 293, 339, 391, 450, 515, 591, 675, 771, 878, 999, 1135, 1289, 1460, 1652, 1868, 2108, 2376, 2676, 3009, 3379, 3793, 4250, 4760, 5325, 5952

Offset

0,7

Links

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

Example

a(9) counts these 5 partitions:  9, 81, 72, 63, 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, A241088.

Sequence in context: A141283 A276828 A309715 * A186445 A080078 A036415

Adjacent sequences: A241086 A241087 A241088 * A241090 A241091 A241092

Keyword

nonn,easy

Author

Clark Kimberling, Apr 17 2014

Status

approved