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

0,4

Comments

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

Links

Table of n, a(n) for n=0..56.

Leroy Quet, Integers Arranged: Q & Puzzle

Example

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

Prog

(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

Crossrefs

a(n) <= A063865(n).

Sequence in context: A033461 A143432 A137677 * A225869 A039972 A344834

Adjacent sequences: A015815 A015816 A015817 * A015819 A015820 A015821

Keyword

nonn

Author

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

Extensions

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

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

Status

approved