login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A241412 Number of partitions of n such that neither the number of parts having multiplicity >1 nor the number of distinct parts is a part. 6
1, 0, 1, 1, 3, 2, 4, 4, 7, 7, 11, 14, 19, 21, 30, 38, 51, 59, 81, 98, 124, 156, 199, 239, 311, 365, 468, 572, 711, 844, 1070, 1271, 1572, 1884, 2318, 2749, 3387, 4000, 4879, 5796, 6977, 8266, 9986, 11769, 14071, 16632, 19800, 23300, 27700, 32471, 38447 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

As used here, the term "distinct parts" includes each number, once, that occurs more than once; e.g., the distinct parts of the partition {4,3,3,1,1,1} are 4, 3, 1.

LINKS

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

EXAMPLE

a(6) counts these 4 partitions:  6, 51, 33, 222.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];

Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}]  (* A241408 *)

Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241409 *)

Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)

Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411  *)

Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412  *)

CROSSREFS

Cf. A241408, A241409, A241410, A241411.

Sequence in context: A175512 A240829 A284013 * A241445 A147604 A095401

Adjacent sequences:  A241409 A241410 A241411 * A241413 A241414 A241415

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 22 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 January 22 08:31 EST 2021. Contains 340360 sequences. (Running on oeis4.)