login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A241509 Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of 1s) is not a part. 5
1, 0, 2, 2, 3, 2, 4, 5, 9, 10, 16, 20, 27, 31, 48, 53, 72, 92, 118, 143, 186, 220, 288, 356, 434, 523, 675, 792, 989, 1205, 1469, 1754, 2165, 2565, 3133, 3752, 4498, 5345, 6496, 7629, 9126, 10869, 12890, 15212, 18114, 21220, 25163, 29611, 34783, 40756, 48058 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..50.

FORMULA

a(n) + A241510(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 4 partitions:  6, 33, 222, 111111.

MATHEMATICA

z = 52; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] ==       1 &]]];

Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]]], {n, 0, z}]  (* A241506 *)

Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241507 *)

Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241508 *)

Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241509 *)

Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241510 *)

CROSSREFS

Cf. A241506, A241507, A241508, A241510, A000041.

Sequence in context: A305894 A305811 A239471 * A268327 A053023 A153725

Adjacent sequences:  A241506 A241507 A241508 * A241510 A241511 A241512

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 24 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)