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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282892 The difference between the number of partitions of n into odd parts (A000009) and the number of partitions of n into even parts (A035363). 2
0, 1, 0, 2, 0, 3, 1, 5, 1, 8, 3, 12, 4, 18, 7, 27, 10, 38, 16, 54, 22, 76, 33, 104, 45, 142, 64, 192, 87, 256, 120, 340, 159, 448, 215, 585, 283, 760, 374, 982, 486, 1260, 634, 1610, 814, 2048, 1049, 2590, 1335, 3264, 1700, 4097, 2146, 5120, 2708, 6378, 3390, 7917, 4243, 9792, 5276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Robert G. Wilson v and Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n=1..165 from Robert G. Wilson v)

FORMULA

a(2n-1) = A000009(2n-1) = A078408(n).

a(2n) = A282893(n).

MAPLE

with(numtheory):

b:= proc(n, t) option remember; `if`(n=0, 1, add(add(`if`(

      (d+t)::odd, d, 0), d=divisors(j))*b(n-j, t), j=1..n)/n)

    end:

a:= n-> b(n, 0) -b(n, 1):

seq(a(n), n=0..80);  # Alois P. Heinz, Feb 24 2017

MATHEMATICA

f[n_] := Length[ IntegerPartitions[n, All, 2Range[n] -1]] - Length[ IntegerPartitions[n, All, 2 Range[n]]]; Array[f, 60]

CROSSREFS

Cf. A000009, A035363, A078408, A282893.

Sequence in context: A180876 A162170 A266770 * A008798 A005290 A326440

Adjacent sequences:  A282889 A282890 A282891 * A282893 A282894 A282895

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Feb 24 2017

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 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)