A063867 Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = 0 or +- 1.

1, 2, 2, 2, 2, 6, 10, 8, 14, 46, 80, 70, 124, 442, 794, 722, 1314, 4820, 8882, 8220, 15272, 56920, 106444, 99820, 187692, 707486, 1336546, 1265204, 2399784, 9119656, 17358560, 16547220, 31592878, 120801376, 231266520, 221653776

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..3339 (terms < 10^1000; first 101 terms from T. D. Noe)
• Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]

Crossrefs

Cf. A025591, A063865, A063866.

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, 0]+2f[n, 1]

Formula

a(n) = A063865(n) + 2*A063866(n).

Extensions

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