A064381 Number of subsets of {2,...,n} such that the product of their elements is congruent to 0 (mod n+1).

0, 0, 0, 6, 0, 24, 32, 120, 0, 792, 0, 2016, 5760, 13056, 0, 55136, 0, 226944, 387072, 523776, 0, 4112000, 5767168, 8386560, 30408704, 58669056, 0, 259541376, 0, 1062731776, 1609039872, 2147450880, 7927234560, 17103136768, 0, 34359607296, 103054049280

Offset

2,4

Comments

a(n-1) = 0 for prime n.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Example

a(5) = 6 because there are 6 subsets of {2,3,4,5} such that the product of their elements is congruent to 0 (mod 6): {3,4,5}, {2,3,4,5}, {3,4}, {2,3}, {2,3,4}, {2,3,5}.

Maple

a:= proc(n) option remember; local m, b; m, b:= n+1,
      proc(n, p) option remember; `if`(p=0, 2^(n-1),
       `if`(n<2, 0, b(n-1, p)+b(n-1, p*n mod m)))
      end: forget(b): b(n, 1)
    end:
seq(a(n), n=2..50);  # Alois P. Heinz, May 26 2013, revised Apr 25 2022

Mathematica

b[n_, p_, m_] := b[n, p, m] = If[p == 0, 2^(n-1),
     If[n < 2, 0, b[n-1, p, m] + b[n-1, Mod[p*n , m], m]]];
a[n_] := b[n, 1, n+1];
Table[a[n], {n, 2, 50}] (* Jean-François Alcover, Apr 25 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000048.

Sequence in context: A082731 A272673 A167357 * A062254 A028849 A287470

Adjacent sequences: A064378 A064379 A064380 * A064382 A064383 A064384

Keyword

nonn

Author

Vladeta Jovovic, Sep 27 2001

Extensions

More terms from Naohiro Nomoto, Oct 01 2001

Extended beyond a(24) by Alois P. Heinz, May 26 2013

Status

approved