Number of partitions of n into distinct parts of which the number of even parts is not a part.

3

`%I #6 Apr 22 2014 01:31:13
`

`%S 0,1,1,1,2,2,2,3,3,5,5,7,8,11,12,15,18,22,27,31,37,43,52,59,71,82,97,
`

`%T 110,128,148,173,197,225,260,298,339,386,442,502,570,644,733,829,935,
`

`%U 1052,1190,1339,1504,1687,1897,2128,2380,2659,2976,3325,3704,4127
`

`%N Number of partitions of n into distinct parts of which the number of even parts is not a part.
`

`%F a(n) + A240573(n) = A000009(n) for n >= 1.
`

`%e a(9) counts these 5 partitions: 9, 72, 63, 54, 531.
`

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

`%t t1 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240869 *)
`

`%t t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240870 *)
`

`%Y Cf. A240870, A240573, A000009.
`

`%K nonn,easy
`

`%O 0,5
`

`%A _Clark Kimberling_, Apr 14 2014
`

Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents

The OEIS Community | Maintained by The OEIS Foundation Inc.