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!)
A241377 Number of partitions of n such that the number of parts is a part and the number of distinct parts is a part. 5
0, 1, 0, 1, 0, 1, 2, 2, 3, 4, 5, 6, 8, 11, 12, 16, 20, 27, 31, 40, 49, 59, 72, 95, 110, 133, 164, 196, 237, 289, 351, 410, 502, 595, 704, 843, 1009, 1193, 1422, 1658, 1983, 2332, 2744, 3204, 3796, 4459, 5189, 6083, 7116, 8292, 9677, 11222, 13041, 15235 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) + A241378(n) + A241379(n) = A241381(n) for n >= 0.

EXAMPLE

a(9) counts these 4 partitions:  72, 531, 432, 4311.

MATHEMATICA

z = 70; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]];

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241377 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241378 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241379 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241380 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *)

CROSSREFS

Cf. A241378, A241379, A241380, A241381.

Sequence in context: A063595 A316080 A130082 * A266750 A143065 A192660

Adjacent sequences:  A241374 A241375 A241376 * A241378 A241379 A241380

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 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 May 31 12:48 EDT 2020. Contains 334748 sequences. (Running on oeis4.)