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

 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] (* Second program: *) b[n_, t_] := b[n, t] = If[n == 0, 1, Sum[Sum[If[      OddQ[d+t], d, 0], {d, Divisors[j]}]*b[n-j, t], {j, 1, n}]/n]; a[n_] := b[n, 0] - b[n, 1]; a /@ Range[0, 80] (* Jean-François Alcover, Jun 06 2021, after Alois P. Heinz *) 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.

Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)