The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A282892 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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).
(history; published version)

#16 by Alois P. Heinz at Fri Oct 27 20:47:59 EDT 2023

STATUS

editing

approved

#15 by Alois P. Heinz at Fri Oct 27 20:47:57 EDT 2023

LINKS

Robert G. Wilson v and Alois P. Heinz, <a href="/A282892/b282892.txt">Table of n, a(n) for n = 0..10000</a> (terms n=1..165 from Robert G. Wilson v)

STATUS

approved

editing

#14 by Peter Luschny at Sun Jun 06 04:14:14 EDT 2021

STATUS

proposed

approved

#13 by Jean-François Alcover at Sun Jun 06 03:44:43 EDT 2021

STATUS

editing

proposed

#12 by Jean-François Alcover at Sun Jun 06 03:44:35 EDT 2021

MATHEMATICA

(* 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 *)

STATUS

approved

editing

#11 by OEIS Server at Fri Feb 24 16:24:00 EST 2017

LINKS

Robert G. Wilson v and Alois P. Heinz, <a href="/A282892/b282892_1.txt">Table of n, a(n) for n = 0..10000</a> (terms n=1..165 from Robert G. Wilson v)

#10 by Alois P. Heinz at Fri Feb 24 16:24:00 EST 2017

STATUS

editing

approved

Discussion

Fri Feb 24

16:24

OEIS Server: Installed new b-file as b282892.txt.  Old b-file is now b282892_1.txt.

#9 by Alois P. Heinz at Fri Feb 24 16:23:39 EST 2017

LINKS

Robert G. Wilson v, and Alois P. Heinz, <a href="/A282892/b282892_1.txt">Table of n, a(n) for n = 0..10000</a> (terms n=1..165</a> from Robert G. Wilson v)

#8 by Alois P. Heinz at Fri Feb 24 15:46:21 EST 2017

DATA

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

OFFSET

1,3

0,4

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

STATUS

proposed

editing

#7 by Robert G. Wilson v at Fri Feb 24 11:12:27 EST 2017

STATUS

editing

proposed