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 A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 3 18:44 EDT 2023. Contains 363116 sequences. (Running on oeis4.)