A334125 Number of subsets of {1, 3, ..., 2*n-1} which sum to 0 modulo 2*n-1.

2, 2, 2, 2, 4, 6, 10, 18, 30, 54, 98, 178, 328, 608, 1130, 2114, 3974, 7490, 14170, 26890, 51150, 97542, 186420, 356962, 684784, 1315870, 2532410, 4880646, 9418806, 18199014, 35204650, 68174116, 132152842, 256415958, 497967282, 967879954, 1882725390, 3665038872

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

If 2*k - 1 is a prime, then a(k) = (2^k - 2*(-1)^floor(k/2))/(2*k - 1).

Conjecture: a(n) = 2*abs(A178738(n)).

Example

a(5) = 4 because there are 4 subsets of {1, 3, 5, 7, 9} which sum to 0 modulo 9: {}, {9}, {1, 3, 5}, {1, 3, 5, 9}.

Maple

f:= proc(n) local V, k;
  V:= Vector(2*n-1);
  V[2*n-1]:= 1;
  for k from 1 to 2*n-1 by 2 do
    V:= V + V[[$(k+1)..(2*n-1), $1..k]]
  od;
  V[2*n-1]
end proc:
map(f, [$1..40]); # Robert Israel, May 12 2020

Prog

(PARI) a(n) = {my(v=Vec(prod(i=1, n, x^(2*i-1)+1))); sum(i=0, n^2\(2*n-1), v[n^2+1-i*(2*n-1)]); }

Crossrefs

Cf. A063776, A178738.

Sequence in context: A032600 A103260 A060824 * A364811 A244459 A064849

Adjacent sequences: A334122 A334123 A334124 * A334126 A334127 A334128

Keyword

nonn

Author

Jinyuan Wang, Apr 30 2020

Status

approved