A063890 Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = n.

1, 1, 0, 0, 2, 3, 0, 0, 12, 21, 0, 0, 113, 202, 0, 0, 1218, 2241, 0, 0, 14326, 26776, 0, 0, 177714, 335607, 0, 0, 2287975, 4353975, 0, 0, 30282850, 57965473, 0, 0, 409476546, 787414730, 0, 0, 5631955466, 10870618388, 0, 0, 78545902971, 152074824054, 0, 0

Offset: 0

Author

Vladeta Jovovic, Aug 28 2001

Keywords

• nonn

Examples

			a(8) = 12 because 8 = 1+2+3+4+5-6+7-8 = -1+2+3+4-5+6+7-8 = 1-2+3-4+5+6+7-8 = -1-2-3+4+5+6+7-8 = -1+2+3+4+5-6-7+8 = 1-2+3+4-5+6-7+8 = 1+2-3-4+5+6-7+8 = -1-2+3-4+5+6-7+8 = 1+2-3+4-5-6+7+8 = -1-2+3+4-5-6+7+8 = -1+2-3-4+5-6+7+8 = 1-2-3-4-5+6+7+8.
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A025591, A063865-A063867.

Programs

Mathematica

f[n_, s_] := f[n, s]=Which[n==0, If[s==0, 1, 0], Abs[s]>(n*(n+1))/2, 0, True, f[n-1, s-n]+f[n-1, s+n]]; a[n_] := f[n, n]
nmax = 44; d = {1}; a1 = {1};
Do[
  d = PadLeft[d, Length[d] + 2 n] + PadRight[d, Length[d] + 2 n];
  i = Ceiling[Length[d]/2] + n;
  AppendTo[a1, If[i > Length[d], 0, d[[i]]]];
  , {n, nmax}];
a1 (* Ray Chandler, Mar 25 2014 *)

Formula

a(n) = [x^n] Product_{k=1..n} (x^k + 1/x^k). - Ilya Gutkovskiy, Jan 28 2022

Extensions

More terms from Dean Hickerson, Aug 30 2001