A015818 Number of solutions of +- 1 +- 2 +- ... +- (n-1) +- n = 0 in which the partial sums +- 1 +- ... +- k (1<=k<=n) are all distinct.

1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 10, 14, 0, 0, 36, 40, 0, 0, 134, 258, 0, 0, 702, 1040, 0, 0, 4170, 5996, 0, 0, 23642, 36616, 0, 0, 140500, 217002, 0, 0, 852132, 1374692, 0, 0, 5411800, 8852230, 0, 0, 35764246, 56370054, 0, 0, 232969442, 376479130, 0, 0, 1555855594, 2534308444

Offset: 0

Author

Leroy Quet, Christian G. Bower and I. J. Kennedy, Nov 26 2002

Keywords

• nonn

Comments

If n==1 or 2 (mod 4) then a(n)=0.

Examples

			For n=4 there are 2 solutions: +1-2-3+4=0 and -1+2+3-4=0.
		

Links

• Leroy Quet, Integers Arranged: Q & Puzzle

Crossrefs

a(n) <= A063865(n).

Programs

PARI

issol(i, n) = {b = binary(i); while(length(b) < n, b = concat(0, b)); if (! sum(k=1, n, if (b[k], k, -k)), vsp = []; lastnb = 0; for (j=1, n, vsp = Set(concat(vsp, sum(k=1, j, if (b[k], k, -k)))); if (#vsp == lastnb, return (0)); lastnb = #vsp;); return (1););}
a(n) = if ((!n) || ((n % 4) != 1) && ((n % 4) != 2), sum(i=0, 2^n-1, issol(i, n)));  \\ Michel Marcus, May 22 2014

Extensions

a(36)-a(46) from Ray Chandler, Nov 29 2008

a(47)-a(58) from Sean A. Irvine, Dec 13 2018