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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A241506 Number of partitions of n such that (number parts having multiplicity 1) is a part and (number of 1s) is a part. 10
0, 1, 0, 1, 1, 1, 2, 3, 5, 7, 11, 12, 17, 25, 32, 40, 54, 73, 95, 123, 152, 195, 252, 319, 395, 491, 624, 759, 951, 1167, 1446, 1767, 2147, 2631, 3212, 3881, 4684, 5672, 6848, 8215, 9825, 11809, 14070, 16818, 19957, 23737, 28169, 33377, 39357, 46546, 54814 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

FORMULA

a(n) + A241507(n) + A241508(n) = A241510(n) for n >= 0.

EXAMPLE

a(6) counts these 2 partitions:  51, 2211.

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. A241507, A241508, A241509, A241510.

Sequence in context: A139749 A178357 A205667 * A165132 A193063 A039715

Adjacent sequences:  A241503 A241504 A241505 * A241507 A241508 A241509

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 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)