The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A112972 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A112972

Number of ways the set {1,2,...,n} can be split into three subsets of equal sums.
(history; published version)

#32 by Alois P. Heinz at Fri Oct 30 15:01:32 EDT 2020

STATUS

proposed

approved

#31 by Jean-François Alcover at Fri Oct 30 08:40:27 EDT 2020

STATUS

editing

proposed

#30 by Jean-François Alcover at Fri Oct 30 08:40:19 EDT 2020

MATHEMATICA

b[args_List] := b[args] = Module[{nargs = Length[args]}, If[args[[1]] == 0, If[nargs == 2, 1, b[args // Rest]], Sum[If[args[[j]] - Last[args] < 0, 0, b[Append[Sort[Flatten[Table[args[[i]] - If[i == j, Last[args], 0], {i, 1, nargs-1}]]], Last[args]-1]]], {j, 1, nargs-1}]]];

a[n_] := If[Mod[#, 3] == 0, b[{#/3, #/3, #/3, n}]/6, 0]&[n(n+1)/2];

Array[a, 42] (* Jean-François Alcover, Oct 30 2020, after Alois P. Heinz *)

STATUS

approved

editing

#29 by OEIS Server at Mon Sep 30 17:33:58 EDT 2019

LINKS

Alois P. Heinz, <a href="/A112972/b112972_1.txt">Table of n, a(n) for n = 1..125</a>

#28 by Alois P. Heinz at Mon Sep 30 17:33:58 EDT 2019

STATUS

editing

approved

Discussion

Mon Sep 30

17:33

OEIS Server: Installed new b-file as b112972.txt.  Old b-file is now b112972_1.txt.

#27 by Alois P. Heinz at Mon Sep 30 17:33:52 EDT 2019

LINKS

Alois P. Heinz, <a href="/A112972/b112972_1.txt">Table of n, a(n) for n = 1..100125</a>

STATUS

approved

editing

#26 by N. J. A. Sloane at Sat Sep 21 09:43:44 EDT 2019

STATUS

editing

approved

#25 by N. J. A. Sloane at Sat Sep 21 09:43:42 EDT 2019

CROSSREFS

Similar sequences: A327448, A327449, A327450.

STATUS

approved

editing

#24 by Alois P. Heinz at Tue Aug 07 20:19:50 EDT 2018

STATUS

editing

approved

#23 by Alois P. Heinz at Tue Aug 07 20:19:38 EDT 2018

MAPLE

b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local m; m:= n*(n+1)/2; `if`(irem(m, 3)=0, b((m/3)$3, n)/6, 0) end: seq(a(n), n=1..42); # Alois P. Heinz, Sep 03 2009

b:= proc() option remember; local i, j, t; `if`(args[1]=0,

`if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(

`if`(args[j] -args[nargs]<0, 0, b(sort([seq(args[i]-

`if`(i=j, args[nargs], 0), i=1..nargs-1)])[],

args[nargs]-1)), j=1..nargs-1))

end:

a:= n-> (m-> `if`(irem(m, 3)=0, b((m/3)$3, n)/6, 0))(n*(n+1)/2):

seq(a(n), n=1..42); # Alois P. Heinz, Sep 03 2009

STATUS

approved

editing

Discussion

Tue Aug 07

20:19

Alois P. Heinz: ... reformatted ...