A173500 Number of sequences of length n with terms from {0,1,...,n-1} such that the sum of terms is 0 modulo n and the i-th term is not i or 2i modulo n.

0, 0, 0, 6, 64, 854, 13392, 244944, 5124266, 120795956, 3169804000, 91666666668, 2897010809280, 99350833566282, 3674884626652666, 145845089585448960, 6182031393612132352, 278750799336055446646, 13322922112485213149376

Offset: 1

Author

Max Alekseyev, Feb 20 2010

Keywords

• nonn

Examples

			For n=4 the a(4)=6 sequences are 0103, 0112, 0301, 3113, 3302 and 3311. - _Robert Israel_, Aug 30 2020
		

Links

• Robert Israel, Table of n, a(n) for n = 1..200
• Art of Problem Solving forum, 45th IMO Team Selection Test Lincoln, Nebraska.

Crossrefs

Cf. A173499.

Programs

Maple

f:= proc(n)
local g;
  g:= proc(i,s) option remember;
    if i = 0 then if s=0 then return 1 else return 0 fi fi;
    add(procname(i-1,s-k mod n),k= {$0..n-1} minus {2*i mod n,i})
  end proc;
  g(n,0)
end proc:
map(f, [$1..30]); # Robert Israel, Aug 30 2020

Mathematica

f[n_] := Module[{g}, g[i_, s_] := g[i, s] = With[{}, If[i == 0, If[s == 0, Return@1, Return@0]]; Sum[g[i-1, Mod[s-k, n]], {k, Range[0, n-1] ~Complement~ {Mod[2i, n], i}}]]; g[n, 0]];
Table[f[n], {n, 1, 30}] (* Jean-François Alcover, May 11 2023, after Robert Israel *)

Formula

For prime p, a(p) = (p-1)*((p-2)^(p-1)-1)/p.