The OEIS is supported by the many generous donors to the OEIS Foundation.

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

5

`%I #7 Apr 24 2014 10:28:53
`

`%S 0,1,0,1,1,1,1,1,2,2,3,2,3,3,4,5,6,6,7,8,8,10,11,13,14,17,18,21,22,25,
`

`%T 27,31,33,38,42,47,52,57,63,69,76,82,91,99,109,119,132,142,158,171,
`

`%U 188,203,223,240,263,284,309,334,364,393,428,463,501,543,588
`

`%N Number of partitions p of n into distinct parts such that max(p) < 2*(number of parts of p).
`

`%e a(15) counts these 5 partitions: 7521, 7431, 6531, 6432, 54321.
`

`%t z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
`

`%t Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)
`

`%t Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
`

`%t Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
`

`%t Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
`

`%t Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)
`

`%Y Cf. A241086, A241087, A241088, A241089.
`

`%K nonn,easy
`

`%O 0,9
`

`%A _Clark Kimberling_, Apr 17 2014
`