A113037 Number of solutions to +- 1 +- 2 +- .. +- n = 3.

0, 0, 1, 0, 0, 3, 5, 0, 0, 23, 39, 0, 0, 219, 396, 0, 0, 2406, 4435, 0, 0, 28431, 53167, 0, 0, 353500, 667874, 0, 0, 4557831, 8675836, 0, 0, 60382450, 115601178, 0, 0, 816998489, 1571272955, 0, 0, 11242173783, 21701318843, 0, 0, 156841667096

Offset: 0

Author

Floor van Lamoen, Oct 11 2005

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 0..3340 (terms < 10^1000)

Crossrefs

Cf. A058377, A063865, A063866.

Programs

Maple

A113037:= 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,3); od; t; end;

Mathematica

nmax = 50; d = {1}; a1 = {};
Do[
  i = Ceiling[Length[d]/2] + 3;
  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) is the coefficient of x^3 in product(x^(-k)+x^k, k=1..n).