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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240058 Number of partitions of n such that m(1) = m(3), where m = multiplicity. 3
1, 0, 1, 0, 3, 1, 4, 2, 8, 5, 12, 9, 21, 17, 32, 29, 52, 49, 79, 79, 123, 126, 184, 195, 278, 299, 409, 449, 603, 668, 874, 979, 1263, 1423, 1803, 2045, 2563, 2916, 3608, 4121, 5056, 5783, 7029, 8055, 9725, 11151, 13366, 15337, 18285, 20979, 24871, 28535 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..52.

FORMULA

a(n) = A182714(n+3) - A182714(n) = A240059(n+1) - A240059(n) for n >= 0.

EXAMPLE

a(6) counts these 4 partitions:  6, 42, 321, 222.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 1] < Count[p, 3]], {n, 0, z}]  (* A182714 *)

t2 = Table[Count[f[n], p_ /; Count[p, 1] <= Count[p, 3]], {n, 0, z}] (* A182714(n+3) *)

t3 = Table[Count[f[n], p_ /; Count[p, 1] == Count[p, 3]], {n, 0, z}] (* A240058 *)

t4 = Table[Count[f[n], p_ /; Count[p, 1] > Count[p, 3]], {n, 0, z}]  (* A240059 *)

t5 = Table[Count[f[n], p_ /; Count[p, 1] >= Count[p, 3]], {n, 0, z}] (* A240059(n+1) *)

CROSSREFS

Cf. A182714, A240059, A000041.

Sequence in context: A115659 A067060 A068028 * A275896 A163359 A065256

Adjacent sequences:  A240055 A240056 A240057 * A240059 A240060 A240061

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 31 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 December 6 09:25 EST 2019. Contains 329791 sequences. (Running on oeis4.)