A063866 Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = 1.

0, 1, 1, 0, 0, 3, 5, 0, 0, 23, 40, 0, 0, 221, 397, 0, 0, 2410, 4441, 0, 0, 28460, 53222, 0, 0, 353743, 668273, 0, 0, 4559828, 8679280, 0, 0, 60400688, 115633260, 0, 0, 817175698, 1571588177, 0, 0, 11243980807, 21704569869, 0, 0, 156860869714

Offset: 0

Author

N. J. A. Sloane, following a suggestion by J. H. Conway, Aug 27 2001

Keywords

• nonn
• easy
• nice

Links

• Ray Chandler, Table of n, a(n) for n = 0..3340 (terms < 10^1000; first 101 terms from T. D. Noe)

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, 1]
nmax = 50; d = {1}; a1 = {};
Do[
  i = Ceiling[Length[d]/2] + 1;
  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 *)

Formula

a(n) equals the coefficient of x in Product_{k=1..n} (x^k + 1/x^k). - Paul D. Hanna, Jul 10 2018

Extensions

More terms from Dean Hickerson and Vladeta Jovovic, Aug 28 2001