A113036 Number of solutions to +- 1 +- 2 +- .. +- n = 2.

0, 0, 0, 1, 2, 0, 0, 8, 13, 0, 0, 69, 123, 0, 0, 719, 1313, 0, 0, 8215, 15260, 0, 0, 99774, 187615, 0, 0, 1264854, 2399207, 0, 0, 16544234, 31587644, 0, 0, 221625505, 425313967, 0, 0, 3025271756, 5829531261, 0, 0, 41929052284, 81066732018, 0

Offset

0,5

Links

Ray Chandler, Table of n, a(n) for n = 0..3339 (terms < 10^1000)

Formula

a(n) is the coefficient of x^2 in product(x^(-k)+x^k, k=1..n).

Maple

A113036:= proc(n) local i, j, p, t; t:= NULL; for j to n do p:=1; for i to j do p:=p*(x^(-i)+x^i); od; t:=t, coeff(p, x, 2); od; t; end;

Mathematica

nmax = 50; d = {1}; a1 = {};
Do[
  i = Ceiling[Length[d]/2] + 2;
  AppendTo[a1, If[i > Length[d], 0, d[[i]]]];
  d = PadLeft[d, Length[d] + 2 n] + PadRight[d, Length[d] + 2 n];
  , {n, nmax}];
a1 (* Ray Chandler, Mar 14 2014 *)

Crossrefs

Cf. A058377, A063865, A063866.

Sequence in context: A235789 A236925 A134414 * A000425 A230878 A349369

Adjacent sequences: A113033 A113034 A113035 * A113037 A113038 A113039

Keyword

nonn

Author

Floor van Lamoen, Oct 11 2005

Status

approved