A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.

0, 0, 1, 1, 1, 1, 5, 11, 10, 1, 79, 165, 1, 664, 2917, 3308, 9295, 23729, 31874, 301029, 422896, 1, 13716866, 71504979, 100664384, 54148590, 880696661, 498017758, 27450476786, 111911522818, 179459955553, 2144502175213, 59115423982, 45837019664551

Offset

1,7

Comments

For n=7 we have splittings 761/5432, 752/6431, 743/6521, 7421/653 and 7/61/52/43 so a(7)=5.

a(n) = 1 <=> n*(n+1)/2 is product of two primes. - Alois P. Heinz, Sep 03 2009

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A035470(n) - 1. - Franklin T. Adams-Watters, Jun 02 2006

Maple

with(numtheory): b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local i, m, x; m:= n*(n+1)/2; add(b(i$(m/i), n)/(m/i)!, i=[select(x-> x>=n, divisors(m) minus {m})[]]) end: seq(a(n), n=1..25);  # Alois P. Heinz, Sep 03 2009

Mathematica

b[args_List] := b[args] = If[args[[1]] == 0, If[Length[args] == 2, 1, b[Rest[args]]], Sum[If[args[[j]] - args[[-1]] < 0, 0, b[Sort[Join[ Table[ args[[i]] - If[i == j, args[[-1]], 0], {i, 1, Length[args] - 1}]]], {args[[-1]] - 1}]], {j, 1, Length[args] - 1}]]; b[a1_List, a2_List] := b[Join[a1, a2]];
a[n_] := a[n] = With[{m = n*(n + 1)/2}, Sum[b[Append[Array[i&, m/i], n]] / (m/i)!, {i, Select[Divisors[m] ~Complement~ {m}, # >= n&]}]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 22 2017, after Alois P. Heinz *)

Crossrefs

Cf. A035470.

Cf. A164977, A164978. - Alois P. Heinz, Sep 03 2009

Sequence in context: A075261 A254766 A185201 * A258995 A335554 A157801

Adjacent sequences: A112953 A112954 A112955 * A112957 A112958 A112959

Keyword

nonn

Author

Floor van Lamoen, Oct 07 2005

Extensions

More terms from Franklin T. Adams-Watters, Jun 02 2006

a(19)-a(33) from Alois P. Heinz, Sep 03 2009

a(34) from Alois P. Heinz, Aug 06 2016

Status

approved